In this blog, we will delve into the intricacies of forward propagation, its calculation process, and its significance in different types of neural networks, including feedforward propagation, CNNs, and ANNs.
We will also explore the components involved, such as activation functions, weights, and biases, and discuss its applications across various domains, including trading. Additionally, we will discuss the examples of forward propagation implemented using Python, along with potential future developments and FAQs.
This blog covers:
For centuries, we've been fascinated by how the human mind works. Philosophers have long grappled with understanding human thought processes. However, it's only in recent years that we've started making real progress in deciphering how our brains operate. This is where conventional computers diverge from humans.
You see, while we can create algorithms to solve problems, we have to consider all sorts of probabilities. Humans, on the other hand, can start with limited information and still learn and solve problems quickly and accurately. Hence, we began researching and developing artificial brains, now known as neural networks.
A neural network is a computational model inspired by the human brain's neural structure, consisting of interconnected layers of artificial neurons. These networks process input data, adjust through learning, and produce outputs, making them effective for tasks like pattern recognition, classification, and predictive modelling.
A neural network could be simply described as follows:
One popular application of neural networks is image recognition software, capable of identifying faces and tagging the same person in different lighting conditions.
Now, let's delve into the details of forward propagation beginning with its definition.
Forward propagation is a fundamental process in neural networks that involves moving input data through the network to produce an output. It's essentially the process of feeding input data into the network and computing an output value through the layers of the network.
During forward propagation, each neuron in the network receives input from the previous layer, performs a computation using weights and biases, applies an activation function, and passes the result to the next layer. This process continues until the output is generated. In simple terms, forward propagation is like passing a message through a series of people, with each person adding some information before passing it to the next person until it reaches its destination.
Next, we will see the forward propagation algorithm in detail.
Here's a simplified explanation of the forward propagation algorithm:
The output of the neural network is then compared to the actual output (in the case of supervised learning) to calculate the error. This error is then used to adjust the weights and biases of the network during the backpropagation phase, which is crucial for training the neural network.
I will explain forward propagation with the help of a simple equation of a line next.
We all know that a line can be represented with the help of the equation:
y = mx + b
Where,
But why are we jotting the line equation here?
This will help us later on when we understand the components of a neural network in detail.
Remember how we said neural networks are supposed to mimic the thinking process of humans?
Well, let us just assume that we do not know the equation of a line, but we do have graph paper and draw a line randomly on it.
For the sake of this example, you drew a line through the origin and when you saw the x and y coordinates, they looked like this:
This looks familiar. If I asked you to find the relation between x and y, you would directly say it is y = 3x. But let us go through the process of how forward propagation works. We will assume here that x is the input and y is the output.
The first step here is the initialisation of the parameters. We will guess that y must be a multiplication factor of x. So we will assume that y = 5x and see the results then. Let us add this to the table and see how far we are from the answer.
Note that taking the number 5 is just a random guess and nothing else. We could have taken any other number here. I should point out that here we can term 5 as the weight of the model.
All right, this was our first attempt, now we will see how close (or far) we are from the actual output. One way to do that is to use the difference between the actual output and the output we calculated. We will call this the error. Here, we aren’t concerned with the positive or negative sign and hence we take the absolute difference of the error.
Thus, we will update the table now with the error.
If we take the sum of this error, we get the value 30. But why did we total the error? Since we are going to try multiple guesses to come to the closest answer, we need to know how close or how far we were from the previous answers. This helps us refine our guesses and calculate the correct answer.
Wait. But if we just add up all the error values, it feels like we are giving equal weightage to all the answers. Shouldn’t we penalise the values which are way off the mark? For example, 10 here is much higher than 2. It is here that we introduce the somewhat famous “Sum of squared Errors” or SSE for short. In SSE, we square all the error values and then add them. Thus, the error values which are very high get exaggerated and thus, help us in knowing how to proceed further.
Let’s put these values in the table below.
Now the SSE for the weight 5 (Recall that we assumed y = 5x), is 145. We call this the loss function. The loss function is important to understand the efficiency of the neural network and also helps us when we incorporate backpropagation in the neural network.
All right, so far we understood the principle of how the neural network tries to learn. We have also seen the basic principle of the neuron. Next, we will see the forward vs backward propagation in the neural network.
Below is the table for a clear difference between forward and backward propagation in the neural network.
Aspect 
Forward Propagation 
Backward Propagation 
Purpose 
Compute the output of the neural network given inputs 
Adjust the weights of the network to minimise error 
Direction 
Forward from input to output 
Backwards, from output to input 
Calculation 
Computes the output using current weights and biases 
Updates weights and biases using calculated gradients 
Information flow 
Input data > Output data 
Error signal > Gradient updates 
Steps 
1. Input data is fed into the network. 2. Data is processed through hidden layers. 3. Output is generated. 
1. Error is calculated using a loss function. 2. Gradients of the loss function are calculated. 3. Weights and biases are updated using gradients. 
Used in 
Prediction and inference 
Training the neural network 
Next, let us see the forward propagation in different types of neural networks.
Forward propagation is a key process in various types of neural networks, each with its own architecture and specific steps involved in moving input data through the network to produce an output.
Forward propagation is a fundamental process in various types of neural networks, including:
Moving forward, let us discuss the components of forward propagation.
In the above diagram, we see a neural network consisting of three layers. The first and the third layer are straightforward, input and output layers. But what is this middle layer and why is it called the hidden layer?
Now, in our example, we had just one equation, thus we have only one neuron in each layer.
Nevertheless, the hidden layer consists of two functions:
Going forward, we must check out the applications of forward propagation to learn about the same in detail.
In this example, we will be using a 3layer network (with 2 input units, 2 hidden layer units, and 2 output units). The network and parameters (or weights) can be represented as follows.
Let us say that we want to train this neural network to predict whether the market will go up or down. For this, we assign two classes Class 0 and Class 1.
Here, Class 0 indicates the data point where the market closes down, and conversely, Class 1 indicates that the market closes up. To make this prediction, a train data(X) consisting of two features x1, and x2. Here x1 represents the correlation between the close prices and the 10day simple moving average (SMA) of close prices, and x2 refers to the difference between the close price and the 10day SMA.
In the example below, the data point belongs to class 1. The mathematical representation of the input data is as follows:
X = [x1, x2] = [0.85,.25] y= [1]
Example with two data points:
$$ X = \begin{bmatrix} x_{11} & x_{12} \\ x_{22} & x_{22} \\ \end{bmatrix} = \begin{bmatrix} 0.85 & 0.25 \\ 0.71 & 0.29 \\ \end{bmatrix} $$$$ Y = \begin{bmatrix} y_1 \\ y_2 \\ \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ \end{bmatrix} $$The output of the model is categorical or a discrete number. We need to convert this output data into a matrix form. This enables the model to predict the probability of a data point belonging to different classes. When we make this matrix conversion, the columns represent the classes to which that example belongs, and the rows represent each of the input examples.
$$ Y = \begin{bmatrix} y_1 \\ y_2 \\ \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 1 & 0 \\ \end{bmatrix} $$In the matrix y, the first column represents class 0 and second column represents class 1. Since our example belongs to Class 1, we have 1 in the second column and zero in the first.
This process of converting discrete/categorical classes to logical vectors/matrices is called OneHot Encoding. It's sort of like converting the decimal system (1,2,3,4....9) to binary (0,1,01,10,11). We use onehot encoding as the neural network cannot operate on label data directly. They require all input variables and output variables to be numeric.
In neural network learning, apart from the input variable, we add a bias term to every layer other than the output layer. This bias term is a constant, mostly initialised to 1. The bias enables moving the activation threshold along the xaxis.
When the bias is negative the movement is made to the right side, and when the bias is positive the movement is made to the left side. So a biassed neuron should be capable of learning even such input vectors that an unbiased neuron is not able to learn. In the dataset X, to introduce this bias we add a new column denoted by ones, as shown below.
$$ X = \begin{bmatrix} x_0 & x_1 & x_2 \\ \end{bmatrix} = \begin{bmatrix} 1 & 0.85 & 0.25 \\ \end{bmatrix} $$Let us randomly initialise the weights or parameters for each of the neurons in the first layer. As you can see in the diagram we have a line connecting each of the cells in the first layer to the two neurons in the second layer. This gives us a total of 6 weights to be initialized, 3 for each neuron in the hidden layer. We represent these weights as shown below.
$$ Theta_1 = \begin{bmatrix} 0.1 & 0.2 & 0.3 \\ 0.4 & 0.5 & 0.6 \\ \end{bmatrix} $$Here, Theta_{1} is the weights matrix corresponding to the first layer.
The first row in the above representation shows the weights corresponding to the first neuron in the second layer, and the second row represents the weights corresponding to the second neuron in the second layer. Now, let’s do the first step of the forward propagation, by multiplying the input value for each example by their corresponding weights which are mathematically shown below.
Theta_{1} * X
Before we go ahead and multiply, we must remember that when you do matrix multiplications, each element of the product, X*θ, is the dot product sum of the row in the first matrix X with each of the columns of the second matrix θ.
When we multiply the two matrices, X and θ, we are expected to multiply the weights with the corresponding input example values. This means we need to transpose the matrix of example input data, X so that the matrix will multiply each weight with the corresponding input correctly.
$$ X_t = \begin{bmatrix} 1 \\ 0.85 \\ 0.25 \\ \end{bmatrix} $$z^{2} = Theta_{1}*X_{t}
Here z^{2} is the output after matrix multiplication, and X_{t} is the transpose of X.
The matrix multiplication process:
$$ \begin{bmatrix} 0.1 & 0.2 & 0.3 \\ 0.4 & 0.5 & 0.6 \\ \end{bmatrix} * \begin{bmatrix} 1 \\ 0.85 \\ 0.25 \\ \end{bmatrix} $$ $$ = \begin{bmatrix} 0.1*1 + 0.2*0.85 + 0.3*0.25 \\ 0.4*1 + 0.5*0.85 + 0.6*0.25 \\ \end{bmatrix} = \begin{bmatrix} 1.02 \\ 0.975 \\ \end{bmatrix} $$Let us say that we have applied a sigmoid activation after the input layer. Then we have to elementwise apply the sigmoid function to the elements in the z² matrix above. The sigmoid function is given by the following equation:
$$ f(x) = \frac{1}{1+e^{x}} $$After the application of the activation function, we are left with a 2x1 matrix as shown below.
$$ a^{(2)} = \begin{bmatrix} 0.735 \\ 0.726 \\ \end{bmatrix} $$Here a^{(2)} represents the output of the activation layer.
These outputs of the activation layer act as the inputs for the next or the final layer, which is the output layer. Let us initialize another random weights/parameters called Theta_{2} for the hidden layer. Each row in Theta_{2} represents the weights corresponding to the two neurons in the output layer.
$$ Theta_2 \begin{bmatrix} 0.5 & 0.4 & 0.3 \\ 0.2 & 0.5 & 0.1 \\ \end{bmatrix} $$After initializing the weights (Theta_{2}), we will repeat the same process that we followed for the input layer. We will add a bias term for the inputs of the previous layer. The a^{(2)} matrix looks like this after the addition of bias vectors:
$$ a^{(2)} = \begin{bmatrix} 1 \\ 0.735 \\ 0.726 \\ \end{bmatrix} $$Let us see how the neural network looks like after the addition of the bias unit:
Before we run our matrix multiplication to compute the final output z³, remember that before in z² calculation we had to transpose the input data a¹ to make it “line up” correctly for the matrix multiplication to result in the computations we wanted. Here, our matrices are already lined up the way we want, so there is no need to take the transpose of the a^{(2)} matrix. To understand this clearly, ask yourself this question: “Which weights are being multiplied with what inputs?”. Now, let us perform the matrix multiplication:
z^{3} = Theta_{2}*a^{(2)} where z^{3} is the output matrix before the application of an activation function.
Here for the last layer, we will be multiplying a 2x3 with a 3x1 matrix, resulting in a 2x1 matrix of output hypotheses. The mathematical computation is shown below:
$$ \begin{bmatrix} 0.5 & 0.4 & 0.3 \\ 0.2 & 0.5 & 0.1 \\ \end{bmatrix} * \begin{bmatrix} 1 \\ 0.735 \\ 0.726 \\ \end{bmatrix} $$ $$ = \begin{bmatrix} 0.5*1 + 0.4*0.735 + 0.3*0.726 \\ 0.2*1 + 0.5*0.735 + 0.1*0.726 \\ \end{bmatrix} = \begin{bmatrix} 1.0118 \\ 0.6401 \\ \end{bmatrix} $$After this multiplication, before getting the output in the final layer, we apply an elementwise conversion using the sigmoid function on the z² matrix.
a^{3} = sigmoid(z^{3})
Where a^{3} denotes the final output matrix.$$ a^3 = \begin{bmatrix} 0.7333 \\ 0.6548 \\ \end{bmatrix} $$
The output of a sigmoid function is the probability of the given example belonging to a particular class. In the above representation, the first row represents the probability that the example belonging to Class 0 and the second row represents the probability of Class 1.
That’s all there is to know about forward propagation in Neural networks. But wait! How can we apply this model in trading? Let’s find out below.
Forward propagation in trading using neural networks involves several steps.
Last but not least, you must keep monitoring the performance of the trading strategy in realworld market conditions and evaluate the profitability and risk of the trading on a continuous basis.
Now that you have understood the steps thoroughly, let us move forward to find the steps of forward propagation for trading with Python.
Below, we will use Python programming to predict the price of our stock “AAPL”. Here are the steps with the code:
This step imports essential libraries required for data processing, fetching stock data, and building a neural network.
In the code, numpy is used for numerical operations, pandas for data manipulation, yfinance to download stock data, tensorflow for creating and training the neural network, and sklearn for splitting data and preprocessing.
The function in the code above uses yfinance to download historical stock data for a specified ticker symbol within a given date range. It returns a DataFrame containing the stock data, which includes information such as the closing prices, which are crucial for subsequent steps.
In this step, the function scales the stock's closing prices to a range between 0 and 1 using MinMaxScaler.
Scaling the data is important for neural network training as it standardises the input values, improving the model's performance and convergence.
This function generates the dataset for training by creating sequences of data points. It takes the scaled data and creates input features (X) and target labels (y). Each input feature is a sequence of time_steps number of past prices, and each target label is the next price following the sequence.
This step involves fetching the historical stock data for Apple Inc. (ticker: AAPL) from January 1, 2010, to May 20, 2024, using the get_stock_data function defined earlier. The fetched data is stored in stock_data.
Here, the closing prices from the fetched stock data are scaled using the preprocess_data function. The scaled data and the scaler used for transformation are returned for future use in rescaling predictions.
In this step, input features and target labels are created using a window of 30 time steps (days). The create_dataset function is used to transform the scaled closing prices into the required format for the neural network.
The dataset is split into training, validation, and test sets. First, 70% of the data is used for training, and the remaining 30% is split equally into validation and test sets. This ensures the model is trained and evaluated on separate data subsets.
This step defines the neural network architecture using TensorFlow's Keras API. The network has three layers: two hidden layers with 64 and 32 neurons respectively, both using the ReLU activation function, and an output layer with a single neuron to predict the stock price.
The neural network model is compiled using the Adam optimizer and mean squared error (MSE) loss function. Compiling configures the model for training, specifying how it will update weights and calculate errors.
In this step, the model is trained using the training data. The training runs for 50 epochs with a batch size of 32. During training, the model also evaluates its performance on the validation data to monitor overfitting.
The trained model is evaluated on the test data to measure its performance. The loss value (mean squared error) is printed to indicate the model's prediction accuracy on unseen data.
Predictions are made using the test data. The predicted scaled prices are transformed back to their original scale using the inverse transformation of the scaler, making them interpretable.
A DataFrame is created to compare the actual and predicted prices, including the difference between them. This comparison allows for a detailed analysis of the model's performance.
Finally, the actual and predicted stock prices are plotted for visual comparison. The plot includes labels and legends for clarity, helping to visually assess how well the model's predictions align with the actual prices.
Output:
Date Actual Price Predicted Price Difference 0 20220328 149.479996 152.107712 2.627716 1 20220329 27.422501 27.685801 0.263300 2 20220330 13.945714 14.447398 0.501684 3 20220331 14.193214 14.936252 0.743037 4 20220401 12.434286 12.938693 0.504407 .. ... ... ... ... 534 20240513 139.070007 136.264969 2.805038 535 20240514 12.003571 12.640266 0.636696 536 20240515 9.512500 9.695284 0.182784 537 20240516 10.115357 9.872525 0.242832 538 20240517 187.649994 184.890900 2.759094
So far we have seen how forward propagation works and how to use it in trading, but there are certain challenges with using the same that we will discuss next so as to remain well aware of the same.
Below are the challenges with forward propagation in trading and also the method for each challenge to be overcome.
Challenges with Forward Propagation in Trading 
Ways to Overcome 
Overfitting: Neural networks may overfit to the training data, resulting in poor performance on unseen data. 
Use techniques such as regularisation (e.g., L1, L2 regularisation) to prevent overfitting. Use dropout layers to randomly drop neurons during training to reduce overfitting. Use early stopping to halt training when the validation loss starts to increase. 
Data Quality: Poor quality or noisy data can negatively impact the performance of the neural network. 
Perform thorough data cleaning and preprocessing to remove outliers and errors. Use feature engineering to extract relevant features from the data. Use data augmentation techniques to increase the size and diversity of the training data. 
Lack of Interpretability: Neural networks are often considered blackbox models, making it difficult to interpret their decisions. 
Use techniques such as SHAP (SHapley Additive exPlanations) or LIME (Local Interpretable Modelagnostic Explanations) to explain the predictions of the neural network. Visualise the learned features and activations to gain insights into the model's decisionmaking process. 
Computational Resources: Training large neural networks on large datasets can require significant computational resources. 
Use techniques such as minibatch gradient descent to train the model on smaller batches of data. Use cloud computing services or GPUaccelerated hardware to speed up training. Consider using pretrained models or transfer learning to leverage models trained on similar tasks or datasets. 
Market Volatility: Sudden changes or volatility in the market can make it challenging for neural networks to make accurate predictions. 
Use ensemble methods such as bagging or boosting to combine multiple neural networks and reduce the impact of individual network errors. Implement dynamic learning rate schedules to adapt the learning rate based on the volatility of the market. Use robust evaluation metrics that account for the uncertainty and volatility of the market. 
Noisy data: Inaccurate or mislabelled data can lead to incorrect predictions and poor model performance. 
Perform thorough data validation and error analysis to identify and correct mislabelled data. Use semisupervised or unsupervised learning techniques to leverage unlabelled data and improve model robustness. Implement outlier detection and anomaly detection techniques to identify and remove noisy data points. 
Coming to the end of the blog, let us see some frequently asked questions while using forward propagation in neural networks for trading.
Below, there is a list of commonly asked questions which can be explored for better clarity on forward propagation.
Q: How can overfitting be addressed in trading neural networks?
A: Overfitting can be addressed by using techniques such as regularisation, dropout layers, and early stopping during training.
Q: What preprocessing steps are required before forward propagation in trading neural networks?
A: Preprocessing steps include data cleaning, normalisation, feature engineering, and splitting the data into training, validation, and test sets.
Q: Which evaluation metrics are used to assess the performance of trading neural networks?
A: Common evaluation metrics include accuracy, precision, recall, F1score, and mean squared error (MSE).
Q: What are some best practices for training neural networks for trading?
A: Best practices include using ensemble methods, dynamic learning rate schedules, robust evaluation metrics, and model interpretability techniques.
Q: How can I implement forward propagation in trading using Python?
A: Forward propagation in trading can be implemented using Python libraries such as TensorFlow, Keras, and scikitlearn. You can fetch historical stock data using yfinance and preprocess it before training the neural network.
Q: What are some potential pitfalls to avoid when using forward propagation in trading?
A: Some potential pitfalls include overfitting to the training data, relying on noisy or inaccurate data, and not considering the impact of market volatility on model predictions.
Forward propagation in neural networks is a fundamental process that involves moving input data through the network to produce an output. It is like passing a message through a series of people, with each person adding some information before passing it to the next person until it reaches its destination.
By designing a suitable neural network architecture, preprocessing the data, and training the model using techniques like backpropagation, traders can make informed decisions and develop effective trading strategies.
You can learn more about forward propagation with our learning track on machine learning and deep learning in trading which consists of courses that cover everything from data cleaning to predicting the correct market trend. It will help you learn how different machine learning algorithms can be implemented in financial markets as well as to create your own prediction algorithms using classification and regression techniques. Enroll now!
Author: Chainika Thakar (Originally written by Varun Divakar and Rekhit Pachanekar)
Note: The original post has been revamped on 20^{th} June 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>In this comprehensive guide, we will delve into the concept of open interest in options trading, exploring its significance, interpretation, practical applications and much more. Moreover, we will demonstrate how Python can be used for analysing and interpreting open interest data, providing traders with valuable insights and tools to enhance their decisionmaking process.
This blog covers:
Options trading is a form of derivative trading that enables traders to participate in the price fluctuations of an underlying asset without the necessity of owning it outright.
In options trading, traders can buy or sell options contracts, which grant them the right, but not the obligation,
Some of the key concepts of options trading are:
Options trading offers several advantages, including:
Options trading strategies for beginners can seem like a daunting task. Having had said that, with the video below, as a beginner you can find out some beginner friendly options trading strategies.
While options trading offers significant opportunities for maximising returns, it also involves risks which we will discuss in detail ahead in the blog.
Moving to the open interest in options trading, let us find out what it means and some key points regarding the same.
Open interest in options trading represents the number of contracts that have been initiated and are still open or not yet closed out by an offsetting trade or have not been exercised.
Unlike volume, which measures the number of contracts traded during a specific period, open interest provides insight into the depth of market interest in a particular option contract.
Understanding open interest is crucial for analysing market trends, identifying potential price movements, and developing effective options trading strategies.⁽¹⁾
Let us move to realworld examples of open interest in options trading.
Let us see some realworld examples taking the references from the news of 2023  2024 and also the example of earnings announcement.
Let's imagine you're interested in Tesla (TSLA) stock and considering buying call options. Call options give you the right, but not the obligation, to buy the stock at a specific price (strike price) by a certain date (expiry).
Scenario: Tesla recently announced a new battery technology that analysts believe will significantly boost the company's future. You suspect the stock price will rise in the coming months.
Open interest analysis:
Interpretation: This rise in open interest suggests a growing number of traders are buying TSLA call options. This could indicate:
Scenario: Apple (AAPL) is about to report quarterly earnings. You're unsure if the stock price will rise or fall after the announcement.
Open interest analysis:
Now we will move forward with the topic and find out about types of open interest in options trading.
In options trading, open interest can be classified into three main types based on its behaviour:
Understanding the behaviour of open interest is essential for analysing market sentiment and making informed trading decisions. By monitoring changes in open interest, traders can gain valuable insights into potential price movements and market trends.
Now we will see the significance of open interest in options trading and learn why open interest is preferred.
The significance of open interest in options trading lies in its ability to provide valuable insights into market sentiment, liquidity, and potential price movements. ⁽¹⁾
Here are some key reasons why open interest is important:
Market Sentiment Analysis:
Liquidity Measurement:
Price Trend Identification:
Going forward, we will discuss the relationship between open interest and price in order to increase the clarity on the topic.
There are three possibilities when it comes to open interest and price, and these are:
Let us see the use of open interest in options trading with Python.
(Credit for the code: Akshay Chaudhary)
Start by importing the necessary Python libraries for data manipulation and visualisation.
Read the CSV files containing the March and April contracts for SBIN, and print the tail of each dataframe to inspect the data.
Output:
Expiry_Date Option_Type Strike_Price Symbol Close OI Date 21Mar2024 28Mar2024 CE 800 SBIN 0.50 11016000 22Mar2024 28Mar2024 CE 800 SBIN 0.30 9654000 26Mar2024 28Mar2024 CE 800 SBIN 0.10 8464500 27Mar2024 28Mar2024 CE 800 SBIN 0.05 6808500 28Mar2024 28Mar2024 CE 800 SBIN 0.05 6636000
Output:
Expiry_Date Option_Type Strike_Price Symbol Close OI Date 19Apr2024 25Apr2024 CE 800 SBIN 0.45 8062500 22Apr2024 25Apr2024 CE 800 SBIN 0.45 5406000 23Apr2024 25Apr2024 CE 800 SBIN 0.45 5134500 24Apr2024 25Apr2024 CE 800 SBIN 0.15 4023000 25Apr2024 25Apr2024 CE 800 SBIN 12.10 745500
Combine the 'OI' columns from both dataframes and visualise the total Open Interest and its 5day moving average.
Output:
The plot of Open Interest (OI) from the combined March and April contracts, along with its 5day moving average, shows fluctuations in trading activity over time for SBIN's 800 Strike Price option contracts.
Two types of OIs in the output above are
Combine the 'Close' columns from both dataframes and create a continuous 'Close' price column. Visualise the close prices and their 5day moving average.
Output:
The plot of the continuous 'Close' price above, created by merging the close prices from March and April contracts, shows price movements over time for SBIN's 800 Strike Price option.
This continuous price column allows for seamless tracking of price changes, highlighting periods of volatility and stability. The 5day moving average smooths out daily fluctuations, offering a clearer view of the underlying price trend and aiding in the identification of sustained movements and potential trend reversals.
Next, we will see the common misconceptions about open interest in options trading. Knowing about these misconceptions will help you be aware of what not to spend your time and effort on.
Below we will see the common misconceptions and the realities of open interest in options trading to make the understanding better.
Misconception 
Reality 
High open interest indicates bullishness, low open interest indicates bearishness 
Open interest alone does not indicate market direction. High open interest could mean either bullishness or bearishness, depending on the context. 
Open interest and volume are the same 
While both open interest and volume reflect market activity, they measure different things. Volume measures the number of contracts traded during a specific period, while open interest represents the total number of outstanding contracts. 
Changes in open interest always predict price movements 
Changes in open interest should be interpreted in conjunction with price movements and other indicators. They do not always predict price movements accurately. 
High open interest means high liquidity 
While high open interest generally indicates liquidity, it doesn't guarantee it. Illiquid options can have high open interest due to large institutional positions. 
Open interest always increases before the expiry 
While open interest often increases as expiration approaches, it can decrease if traders close out positions before expiry. 
Open interest provides information about the option buyer's bias 
Open interest does not differentiate between option buyers and sellers. It reflects the total number of open positions, whether long or short. 
Options with high open interest are always more profitable 
High open interest options may have narrower bidask spreads, but they may not always be more profitable. Profitability depends on various factors, including market conditions and trading strategies. 
Moving forward, we will see the challenges that surround the open interest in options trading.
Below you can see the pitfalls and challenges to be aware of associated with the open interest in options trading.
Let us also see how to overcome these challenges of using open interest further.
Below are the ways to overcome the challenges of using open interest.
We've covered various aspects of open interest in options trading, including its definition, interpretation, significance, and practical applications. By learning how to analyse and interpret open interest data, traders can make more informed decisions and develop effective trading strategies.
Moreover, we've explored the relationship between open interest and price, demonstrating how changes in open interest can signal potential trend reversals or continuations. We've also discussed how Python can be used as a tool for analysing open interest data, providing traders with valuable insights and tools to enhance their decisionmaking process.
Additionally, we've addressed common misconceptions, pitfalls, and challenges associated with open interest, and provided strategies to overcome these challenges. By combining open interest analysis with other indicators and continuously learning and refining trading strategies, traders can improve their ability to navigate the complex world of options trading.
You can learn more about open interest in options trading with the systematic options trading course. Modern trading demands a systematic approach and this course is designed to help you create, backtest, implement, live trade and analyse the performance of options strategy. Learn to shortlist options, find the probability of profit, expected profit, and the payoff for any strategy and explore options trading strategies like a butterfly, iron condor, and spread strategies. Enroll now!
File in the download
Author: Chainika Thakar (Originally written by Varun Divakar)
Note: The original post has been revamped on 13^{th} June 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>This webinar is designed to provide a comprehensive introduction to algorithmic trading using Python. We will explore how to integrate Python with popular trading platforms and brokers, including Interactive Brokers, TradingView, MT5, and Amibroker. Participants will gain practical insights into automating trading strategies and executing trades across different platforms.
Aspiring and professional traders, data scientists, financial technology enthusiasts, Python developers, and anyone interested in leveraging technology to automate trading.
Varun holds a Masters degree in Financial Engineering. He has experience working as a trader, a global macro analyst, and also an algo trading strategist. Currently, working in the Content & Research Team at QuantInsti as a Quantitative Analyst, his contributions help in creating offerings for learners in the domain of algorithmic & quantitative trading.
Rushda is a Technical Content Manager who works in the Quantra Research & Content team at QuantInsti. Her educational background includes a post graduate diploma in financial management. Moreover, she also has handson experience when it comes to trading in equities.
This event was conducted on:
Tuesday, June 18, 2024
10:30 AM ET  7:00 PM IST  9:30 PM SGT
We will cover backtesting, optimisation, and risk management which are the crucial steps to ensure effectiveness and reliability of your automated trading system. Additionally, we will address common mistakes to avoid and provide tips for successful automated forex trading. By the end of this guide, you will have the knowledge and tools to set up your own automated forex trading system and potentially improve your trading efficiency and profitability.
This blog covers:
Forex trading, also known as foreign exchange trading or currency trading, involves buying and selling currency pairs on the foreign exchange market with the aim of increasing value of amount traded. Traders speculate on the price movements of currency pairs, such as EUR/USD or GBP/JPY, and profit from the fluctuations in exchange rates.
Forex trading involves speculating on exchange rates using various currency pairs. Traders buy or sell currency derivatives, such as USD/INR futures, based on their speculation. Additionally, investors use forex trading to hedge against foreign exchange risk.
For example, an Indian manufacturing company expecting a payment of 1 million USD in 3 months may hedge against exchange rate fluctuations by buying future contracts. These contracts allow them to exchange 1 million USD into INR at today's rate, even if the rates at that time are lower. However, a premium is often charged on the contracts, depending on the forward curve.⁽¹⁾
Let us now find out about automated forex trading.
Automated forex trading involves using computer programs, often referred to as trading robots or expert advisors (EAs), to automatically execute trades on the foreign exchange market.
These programs are designed to follow predefined forex trading strategies and criteria, such as price levels and technical indicators, to enter and exit trades without the need for manual intervention.
Automated forex trading can help traders execute trades more efficiently, without being affected by emotions, and can operate 24/7, taking advantage of trading opportunities even when the trader is not available.
An example is a hedge fund that uses automated trading systems to execute large volumes of forex trades quickly and efficiently. These systems can analyse market data and execute trades across multiple currency pairs simultaneously, taking advantage of arbitrage opportunities and price discrepancies across different forex markets.
Going forward, the video below will take you through the intricacies of automating a trading strategy.
Also, there are various types of forex trading strategies that we will discuss next.
Forex trading strategies can be from low to medium to highfrequency trading strategies based on the volumes, capital and infrastructure one has. In highfrequency trading strategies, a very popular strategy on forex instruments uses statistical arbitrage to identify trading opportunities based on market inefficiencies. Such opportunities do not last for more than a fraction of a second but the highspeed systems can often use them on large volumes to earn profits.
For retail traders, medium or lowfrequency trading strategies are more popular and advisable. There are a lot of technical indicators which are used to identify trading opportunities. A few of these indicators are moving averages (EMA and SMA), relative strength index (RSI), and Bollinger Bands. These are the most popular and talked about strategies.
Also, forex trading is usually favourable among a lot of retail traders because of the reasons listed below:
There are other marketneutral and trendfollowing strategies such as pairs trading and turtles trading models, which can be used by medium frequency traders. Currency Futures and Derivatives Pricing models based on Greeks (advanced options trading) can be used to evaluate risks and get involved in forex options trading.⁽²⁾
There are several forex trading strategies which can be utilised. These strategies are mentioned in the video below.
Now, we can move to the benefits of automated forex trading.
Below you can see all the benefits of automated forex trading and why traders prefer it.
However, bear in mind, that while automated systems can reduce human error and execute trades precisely as programmed, they cannot eliminate the risk of slippages. Continuous monitoring is often necessary to manage and mitigate these occurrences, ensuring that trades are executed as planned.
Find out more about the automated trading strategies with the video below and enhance your knowledge regarding automated trading.
Now we can see the working of automated forex trading next.
Automated forex trading allows traders to execute trades more efficiently, without being affected by emotions. Also, automated forex trading can operate continuously, taking advantage of trading opportunities even when the trader is not available.
Below is a stepbystep explanation of the working of automated forex trading.
Traders develop a trading strategy based on various criteria such as technical indicators, price action, or fundamental analysis. The entry/exit rules are defined based on the strategy logic.
The trading strategy is then programmed into a computer program using a trading platform that supports automated trading.
The automated trading system continuously monitors the forex market for trading opportunities based on the predefined strategy.
When the trading system identifies a trading opportunity that matches the criteria of the strategy, it automatically executes buy or sell orders without the need for manual intervention.
Automated trading systems often include risk management features such as stoploss orders and position sizing to help manage risk. These risk management techniques need to be set by the trader based on certain factors such as risk tolerance, trading strategy etc.
Before deploying the automated trading system in live market conditions, traders typically backtest the strategy using historical market data to assess its performance and optimise it for better results.
Once the automated trading system is optimised and tested, it can be deployed to trade live in the forex market. The system will continue to execute trades based on the predefined strategy, 24 hours a day, five days a week, without the need for manual intervention.
We will see some known automated forex trading platforms now.
Below we will see some common limitations of automated forex trading along with the ways that can help overcome the same.
Challenges of Automated Forex Trading 
Explanation 
Strategies to Overcome 
Mechanical Failures 
Automated trading systems are prone to technical failures, such as connectivity issues, computer crashes, or power outages, which can disrupt trade execution. 
Use a reliable internet connection and backup power source. Choose a reputable broker with a reliable trading infrastructure. 
OverOptimisation 
Traders may overoptimize their trading strategies based on past market data, resulting in strategies that perform well in backtests but poorly in live market conditions. 
Regularly review and update trading strategies to ensure they remain effective in current market conditions. Avoid overfitting by using a diverse range of historical data for backtesting. 
Lack of Adaptability 
Automated trading systems may struggle to adapt to changing market conditions or unexpected events, leading to losses during periods of high market volatility. 
Build flexibility into trading strategies to adapt to changing market conditions. Monitor market news and events for potential impacts on trading strategies. 
Dependency on Technology 
Automated trading systems rely heavily on technology, and any disruptions or malfunctions in the trading infrastructure can result in significant financial losses. 
Implement redundancy measures and backup systems to minimise the impact of technical failures. Regularly update software and hardware to maintain optimal performance. 
Monitoring Required 
Despite being automated, trading systems still require regular monitoring to ensure they are functioning correctly and to intervene in case of unexpected market behaviour. 
Set up alerts and notifications to monitor the performance of automated trading systems. Review trading activity regularly and intervene if necessary. 
Market Risks 
Automated trading systems are not immune to market risks, such as slippage, spread widening, and price gaps, which can impact the profitability of trades. 
Implement risk management strategies such as stoploss orders and position sizing. 
Moving forward, we will see the common mistakes committed with an automated forex trading system.
Avoiding the common mistakes mentioned below can help you maximise the effectiveness of your automated forex trading system and minimise potential losses.
We will now move ahead to some frequently asked questions regarding automated forex trading.
Let us find out the answers to some frequently asked questions regarding automated forex trading.
Q: How do I choose a forex broker for automated trading?
A: When choosing a forex broker for automated trading, consider factors such as:
Q: Do I need programming skills for automated forex trading?
A: While programming skills are not mandatory for automated forex trading, they can be beneficial if you want to develop custom trading strategies or modify existing ones. Many trading platforms offer userfriendly interfaces for creating automated trading systems without extensive programming knowledge.
Q: How do I monitor and evaluate my automated trading system?
A: To monitor and evaluate your automated trading system, you should:
Q: Is automated forex trading suitable for beginners?
A: Automated forex trading can be suitable for beginners, as it eliminates the need for manual trade execution and allows traders to benefit from predefined trading strategies. However, beginners should take the time to learn about forex trading strategies, risk management, and market dynamics before using automated trading systems. It is essential to start with small trading sizes and gradually increase exposure as you gain experience.
Automated forex trading offers traders a powerful tool to execute trades efficiently and systematically based on predefined strategies. By automating the trading process, traders can eliminate emotional bias, trade 24/7, and take advantage of backtesting and optimisation to improve their trading performance. However, to succeed in automated forex trading, it is essential to develop a robust trading strategy, implement effective risk management techniques, and continuously monitor and evaluate the performance of your automated trading system.
It is crucial to avoid common pitfalls such as overoptimisation, neglecting risk management, and ignoring market conditions. With careful planning, thorough testing, and ongoing optimisation, automated forex trading can be a helpful tool for forex traders.
You can learn more about automated forex trading using Python programming in this Quantra course which is recommended for both beginner and expert forex traders. You will learn to create a momentum trading strategy using real forex markets data in Python as well as to backtest on the inbuilt platform and analyse the results. Check it out now!
Author: Chainika Thakar (Originally written by Anupriya Gupta)
Note: The original post has been revamped on 6^{th} June 2024 for recentness, and accuracy.
Disclaimer: All data and information provided in this article are for informational purposes only. QuantInsti® makes no representations as to accuracy, completeness, currentness, suitability, or validity of any information in this article and will not be liable for any errors, omissions, or delays in this information or any losses, injuries, or damages arising from its display or use. All information is provided on an asis basis.
]]>The TripleBarrier Method is a new tool in financial machine learning that offers a dynamic approach to creating a prediction feature based on risk management. This method provides traders with a framework to set a prediction feature. It is based on what a trader would do if she set profittaking and stoploss levels that adapt in realtime to changing market conditions.
Unlike traditional trading strategies that use fixed percentages or arbitrary thresholds, the TripleBarrier Method adjusts profittaking and stoploss levels based on price movements and market volatility. It achieves this by employing three distinct barriers around the trade entry point: the upper, lower, and vertical barriers. These barriers determine whether the signal will be long, short, or no position at all.
The upper barrier represents the profittaking level, indicating when traders should consider closing their position to secure gains. On the other hand, the lower barrier serves as the stoploss level, signalling when it's wise to exit the trade to limit potential losses.
What sets the TripleBarrier Method apart is its incorporation of time through the vertical barrier. This time constraint ensures that profittaking or stoploss levels are reached within a specified timeframe; if not, the previous position is held for the next period. You can learn more about it in López de Prado’s (2018) book.
If you have 1 million price returns to convert into a classificationbased prediction feature, you’ll face time efficiency issues while using López de Prado’ (2018) algorithm. Let’s present some CPU limitations regarding that concern.
Time efficiency is an important factor in computing for tasks that range from basic calculations to sophisticated simulations and data processing. Central Processing Units (CPUs) are not without their limitations in terms of time efficiency, particularly when it comes to largescale and highly parallelizable tasks. Let’s talk about CPU time efficiency constraints and how they affect different kinds of computations.
Is there another way?
Yes! Using a GPU. GPU is welldesigned for parallelism. Here, we present the Nvidiabased solution.
New to GPU usage? New to Rapids? New to Numba?
Don’t worry! We've got you covered. Let’s dive into these topics.
When combined, Rapids and Numba, two great libraries in the Python ecosystem, provide a convincing way to speed up tasks involving data science and numerical computing. We'll go over the fundamentals of how these libraries interact and the advantages they offer computational workflows.
Rapids library is an opensource library suite that uses GPU acceleration to speed up machine learning and data processing tasks. Popular Python data science libraries, such as cuDF (GPU DataFrame), cuML (GPU Machine Learning), cuGraph (GPU Graph Analytics), and others, are available in GPUaccelerated versions thanks to Rapids, which is built on top of CUDA. Rapids significantly speeds up data processing tasks by utilizing the parallel processing power of GPUs. This allows analysts and data scientists to work with larger datasets and produce faster results.
Numba is a justintime (JIT) Python compiler that optimizes machine code at runtime from Python functions. Numba is an optimization tool for numerical and scientific computing applications that makes Python code perform and compiled languages like C or Fortran. Developers can achieve significant performance gains for computationally demanding tasks by instructing Numba to compile Python functions into efficient machine code by annotating them with the @cuda.jit decorator.
Rapids and Numba work well together because of their complementary abilities to speed up numerical calculations. While Rapids is great at using GPU acceleration for data processing tasks, Numba uses JIT compilation to optimize Python functions to improve CPUbound computation performance. Developers can use GPU acceleration for dataintensive tasks and maximize performance on CPUbound computations by combining these Python libraries to get the best of both worlds.
The standard workflow when combining Rapids and Numba is to use Rapids to offload data processing tasks to GPUs and use Numba to optimize CPUbound computations. This is how they collaborate:
Preprocessing Data with Rapids: To load, manipulate, and preprocess big datasets on the GPU, use the Rapids cuDF library. Utilize GPUaccelerated DataFrame operations to carry out tasks like filtering, joining, and aggregating data.
The Numba library offers a decorator called @cuda.jit that makes it possible to compile Python functions into CUDA kernels for NVIDIA GPU parallel execution. Conversely, RAPIDS is a CUDAbased opensource software library and framework suite. To speed up data processing pipelines from start to finish, it offers a selection of GPUaccelerated libraries for data science and data analytics applications.
Various data processing tasks can be accelerated by using CUDAenabled GPUs in conjunction with RAPIDS when @cuda.jit is used. For example, to perform computations on GPU arrays, you can write CUDA kernels using @cuda.jit (e.g., using NumPylike syntax). These kernels can then be integrated into RAPIDS workflows for tasks like:
Let’s understand how GPU’s hierarchy works. In GPU computing, particularly in frameworks like CUDA (Compute Unified Device Architecture) used by NVIDIA GPUs, these terms are fundamental to understanding parallel processing:
So, to summarize:
I know you’ve been waiting for this algo! Here we present the code to create a prediction feature based on the triplebarrier method using GPU. Please take into consideration that we have used OHLC data. López de Prado (2018) uses another type of data. We have used Maks Ivanov (2019) code which is CPUbased.
Let’s explain stepwise:
We will now obtain the prediction feature using the triple_barrier_method function
Output the value counts of the prediction feature
References:
Here, you have learned the basics of the triplebarrier method, the Rapids libraries, the Numba library, and how to create a prediction feature based on those things. Now, you might be asking yourself:
What’s next?
How could I profit from this prediction feature to create a strategy and go algo? Well, you can use the prediction feature “y” in data for any supervised machinelearningbased strategy and see what you can get as trading performance!
Don’t know which ML model to use? Don’t worry! We've got you covered!
You can learn from different models in this learning track by Quantra about machine learning and deep learning in trading. Inside this learning track, you can find also this topic in detail within the Feature Engineering course we have.
Ready to trade? Get? Set? Go Algo!
File in the download:
Author: José Carlos Gonzáles Tanaka
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>This article is the final project submitted by the author as a part of his coursework in our algo trading course, the Executive Programme in Algorithmic Trading (EPAT) at QuantInsti. Do check our Projects page and have a look at what our students are building.
Rong Fan holds dual master's degrees in Computer Science and Lightning Science & Technology. With over a decade of experience in the Software Development Life Cycle (SDLC) domain, Rong has published more than 10 academic papers, amassing over 100 citations on Google Scholar. He also holds certifications in Professional Project Management and Professional Scrum Master.
Rong has a deep interest in investment and trading. Since 2017, he has managed a value investmentstyle portfolio that has achieved an approximate compound annual growth rate of 20%, consistently outperforming the S&P 500. In March 2022, he earned a certificate from the Wharton School's "Economics of Blockchain and Digital Assets Certificate Program." That same year, he published an ebook titled “Blockchain Value Investing” (Traditional Chinese Edition) on Kindle.
In 2023, Rong achieved his 'Certificate of Excellence' from QuantInsti's Executive Programme in Algorithmic Trading (EPAT) which he pursued with an aim to systematically learn quantitative methods and apply them to practical investment strategies.
A perpetual contract is a cryptocurrency derivative that is essentially a futures contract that has no expiry date and is settled in cash. It allows traders to speculate on their price movements without owning a specific asset. Trading perpetual contracts has many advantages, such as high leverage, low fees, and a wide range of underlying.
For traditional delivery contracts, since the delivery price is fixed at the spot price, once the futures price deviates significantly from the spot price, arbitrage trading will automatically bring the spot price closer. Perpetual contracts have no delivery, so it is impossible to rely on spot arbitrage to increase the recent spot price.
The practice of digital currency exchanges is to pay funding fees between long and short parties every 8 hours. Its basic idea is that within a period of time, if the price of the perpetual contract is higher than the spot price, it means that the bulls have strong momentum, so the longs will pay funding fees to the shorts, and conversely, the shorts will pay funding fees to the longs.
Assuming that the funding rate is 0.01%, then each trader calculates the funds he will pay or receive based on the number of positions. Since the total amount of long and short positions is always equal, the funding fee is not charged by the exchange, but transferred between the long and short parties.
An assumption in statistics that usually means there is no effect or no relationship. In specific statistical testing, the null hypothesis is a contrasting or control hypothesis that assumes that any observed effect or relationship is due to random factors.
In statistical arbitrage, it is sometimes tested whether asset prices follow a mean reversion model. The null hypothesis may be that asset prices do not follow mean reversion, while rejection of the null hypothesis indicates that a mean reversion relationship exists, providing an arbitrage opportunity.
The enhanced DickeyFuller test (Augmented Dickey Fuller) is a modified version of the standard DickeyFuller (standard DickeyFuller). ADF test in pairs trading is used to check the cointegration between two stocks.
The difference
It is a property in time series data that indicates that the roots in the series (with respect to time) remain constant. In statistics, the presence of a unit root indicates that a time series is nonstationary. Specifically, if a time series has a unit root, its mean and variance may increase over time rather than tending to a fixed value.
In statistical arbitrage and time series analysis, understanding the properties of the unit root is crucial to verify the stationarity of the data and to perform effective analysis and model building.
The stationarity of a time series means that a set of time series data looks flat and the statistical characteristics of each order (such as mean, variance, covariance) do not change with time. Typically, stationarity is verified using the Augmented DickeyFuller (ADF) test.
correlation coefficient: 0.99, cointegration test pvalue: 0.2596837
cointegration test p value:, cointegration test pvalue: 0.0
Output
t statistic = 3.3175906010162217
{'1%': 3.4381962830171444, '5%': 2.8650034233058093, '10%': 2.568614210583549}
Since the tstat value is below the critical value of 5%, the spread is considered stationary or cointegrated.
If two or more series are combined and the resulting series is stationary, they are said to be cointegrated. This article only discusses pairs trading, so only twotime series are considered. Nonstationary time series x, y, and the linear combination composed of x, y may also be stationary. In this case, the model is likely to have pseudo (false) regression.
Therefore, the classical model is based on stationary data and requires testing for stationarity on a single series and then testing for cointegration.
2.1.1 Mean Reversion
The trend of mean reversion is that the price moves in a certain relationship around a fixed mean, so first we must make sure that the contract we select must have a stable mean, and the price fluctuations must be around the mean.
2.1.2 Pair trading
Why do we do mean reversion portfolio arbitrage instead of doing mean reversion arbitrage individually for a certain contract? The reason is that the time series of a single futures contract price does not mean reversion in most cases, but the difference (diff) between the prices of two products with a strong correlation is more likely to show a stable mean reversion phenomenon.
Based on the twotime series, take a price difference (diff) sequence, subtract the latest price of the second contract 1hour kline from the latest price sequence K1 of the first contract hour Kline, and get a price difference sequence diff, then we can think the price difference between the two contracts should regress to some extent around the mean of the diff sequence.
We then calculate some theoretical spreads as trading signals. Take two extreme values as the position opening judgment signal, such as the two price differences divided into points of 99% and 1% as the position opening judgment price difference, and use the two values closest to the mean as the position closing signal, such as 52% and 48% The price difference (diff) between the two quantile points is used as the closing judgment price.
The Diff calculation formula is as follows:
Diff = Underlying A  a * Underlying B  constant
2.1.2.1 Example of Pair Trading
The prices of soybean oil and soybean meal themselves may not have a strong mean reversion phenomenon, but what about the price difference between soybean oil and soybean meal? Since the correlation between the two is very strong, they are likely to exhibit a strong mean reversion phenomenon. If their price differences are in line with the mean. Return, then it is feasible to conduct crossvariety arbitrage between the two.
Starting from the next section, we will list the steps, text description, code, and execution results.
Use the Python CCXT package to execute the Binance exchange API to obtain all its perpetual Contract OHLC data.
3.1.1 Data specifications
3.1.2 Part of the code for data acquisition
3.1.3 Data effects
The statistical properties of time series data with stationarity do not change over time, that is, their mean and variance remain unchanged over time.
3.2.1 Stability test code
3.2.2 Stationarity test results
As of December 2023, according to the data results of 3.1, Binance Exchange has a total of 47 groups of perpetual contracts. After the ADF stability test, a total of 3 groups are stationary (as shown below), and the other parts are not stable.
According to the stationarity test results in 3.2.2, ETC, RLC, TRX, BN, TRX, XMR, and XRP are stable time series. Combine them exhaustively and then implement cointegration testing.
3.3.1 Cointegration test code
3.3.2 Cointegration test results
The above figure shows that all pairs conform to the cointegration characteristics.
3.3.3 Test results of cointegration and correlation
After the abovestepDiscover: ETCUSDT, RLCUSDT at the same time conform toCointegration andRelevantrelation. Therefore, Plan to use: ETCUSDT, and RLCUSDT as a trading basis for examples.
3.4.1 Introduction to Principles
For the time series pair selected in 3.3.3, the difference (diff) is consistent with mean regression, so we can take a sequence of differences. Subtract the 1hour close of the first contract from the 1hour close of the second contract to obtain a price difference sequence diff. We can think that the price difference between the two contracts should regress to some extent around the mean of the diff sequence.
Diff = ETC  a * RLC  constant
Next, the values of a and constant need to be calculated.
After calculation in the above example, it is published as follows
a = 11.46
constant = 5.8468
Diff = ETC  11.46 * RLC  constant
3.4.2 Position opening and closing signals
We then calculate some theoretical spreads as trading signals. Take two extreme values as the position opening judgment signal, such as the two price differences divided into points of 99% (top_percentile) and 10% (bottom_percentile) as the position opening judgment price difference, and use the two values closest to the mean as the position closing signal. For example, the two price differences between the 55% and 45% quantile points are used as the takeprofit and exit judgment prices. If the loss is 20%, the stoploss exit will be used.
3.5.1 Pair diff graph
Whether the diff of Pair means reversion is the prerequisite for subsequent operations. Now draw the diff of ETC and RLC as follows.
3.5.2 Stability test of Pair diff
3.5.2.1 Test code
symbol, adf_statistic, p_value, critical_values, is_stationary =
self.analyze_service_instance.stationary_test(df_merged['diff'], "etc_rlc_diff")
3.5.2.2 Test results
As can be seen from the above figure, the pair diff sequence complies with the stationarity test, that is, it complies with mean regression.
3.5.3 Backtesting framework
PyAlgoTrade is a Python library for backtesting stock trading strategies. It is designed to help users evaluate and test their trading strategies using historical data. With PyAlgoTrade, you can verify how your strategy performed under past market conditions, which is crucial for understanding and improving your trading strategy.
Define the parameters of the backtesting framework according to the following trading logic
When there is a position and the diff falls within the following range: [take_profit_left_percentile, take_profit_right_percentile], take profit and exit. For example: take_profit_left_percentile default value: 45%, take_profit_right_percentile default value: 55%.
When there is a position and portfolio_value_change_rate <= stop_loss_portfolio_value_change_percentage, stop loss and exit. For example stop_loss_portfolio_value_change_percentage default value: 30%.
Define the backtest class of PyAlgoTrade
The code is as follows:
Default parameters
This is a good result. Next, we can try to adjust the parameters for further optimization.
Given a parameter range, traverse and repeatedly perform a single backtest to find the optimal parameters, using the Sharpe ratio as the criterion.
Parameter explanation
Since statistics and backtesting framework Python are mainstream, using C# in backtesting requires a lot of reinvention, so it is impossible. But when the premise of obtaining valid parameters, it is feasible to use C# as the live trading language, as long as the live trading logic and backtesting logic are completely consistent. In order to prevent inevitable code deviation, it is still recommended to use the same language and framework to write real code.
Using the parameters in Figure 3.7.1, we can get the trading effect Sharpe ratio: 1.14, and the final market value of the investment portfolio can reach: $90717.54 (initial value: $10000). However, since market styles frequently switch, backtesting is required every once in a while to obtain optimal parameters.
References
This project has detailed crypto perpetual contract pair trading, showcasing the use of statistical arbitrage with Binance data. It gives an endtoend pair trade from idea to backtest, and optimization. We've covered the entire process, from idea to backtesting and optimization, highlighting the importance of robust strategies in cryptocurrency trading.
Feel free to explore our trading projects page to discover more innovative solutions by our talented participants. Use this guide as a valuable resource in your trading journey.
As part of QuantInsti's algo trading course, the Executive Programme in Algortihmic Trading (EPAT), this project reflects the expertise our students achieve. If you too want to learn various aspects of Algorithmic trading then check out EPAT, it equips you with the required skill sets to build a promising career in algorithmic trading. Enroll now!
Disclaimer: The information in this project is true and complete to the best of our Student’s knowledge. All recommendations are made without guarantee on the part of the student or QuantInsti^{®}. The student and QuantInsti^{®} disclaim any liability in connection with the use of this information. All content provided in this project is for informational purposes only and we do not guarantee that by using the guidance you will derive a certain profit.
]]>In this comprehensive guide, we will delve into the world of advanced options trading, covering everything from the overview of advanced options trading to the strategies and the intricacies of their implementation.
As a trader who is knowledgeable about the basics of options trading, this guide will provide you with the skills and insights needed to navigate the complex world of advanced options trading effectively.
This blog covers:
Advanced options trading ventures beyond basic buying and selling of calls and puts. It involves useful combinations of options contracts to achieve specific trading goals.
Let us now see the concepts which are required for advanced options trading.
Essentials while performing the advanced options trading
There are some essentials of advanced options trading and these are:
Strategies involved in advanced options trading
Some common advanced options trading strategies. are:
Also, understanding when to exercise (buy/sell) options early to capture potential benefits or avoid unwanted assignments is crucial in advanced strategies.
Moving forward, let us find out why options trading is so attractive for traders.
Options trading attracts traders for several reasons.
Here's a breakdown of the appeal: ⁽¹⁾
However, it's essential to acknowledge that options trading carries some risks as well. These risks include the potential loss of the entire investment, rapid loss of value due to time decay, and the complexity of options strategies, which may lead to unexpected outcomes.
Therefore, it's crucial for traders to thoroughly understand options trading and employ risk management strategies to protect their investments.
The primary options Greeks are a set of five letters representing key factors that influence the price of an option. These are the essential tools for options traders to analyse and manage risk within their positions. ⁽²⁾
Here's what each Greek signifies:
Moving forward, we will discuss in detail the impact of options Greeks on the options pricing.
Here, we will again see the primary options Greeks, but will discuss the impact of each on the options pricing and also on portfolio management along with an example for each. The options Greeks each have a specific influence on how an option's price reacts to changes in various market factors as well as on the portfolio management.
Options Greeks 
Impact on Options Pricing 
Impact on Portfolio Management 
Example 
Delta 
Measures the rate of change of the option price with respect to changes in the underlying asset price 


Gamma 
Measures the rate of change of Delta with respect to changes in the underlying asset price 


Theta 
Measures the rate of change of the option price with respect to changes in time 


Vega 
Measures the rate of change of the option price with respect to changes in volatility 


Rho 
Measures the rate of change of the option price with respect to changes in interest rates. 


Now we will find out the skills needed for implementing the advanced options trading strategies.
Here are some essential skills you'll need to develop for success with advanced options trading strategies:
Let us now see what putcall parity means and more about the same.
PutCall Parity (PCP) is a relationship between a European call option, a European put option, the underlying asset's price, the riskfree interest rate, and the time to expiration. It essentially states that the price of a call option, adjusted for the present value of the strike price, should be equal to the price of a put option plus the current stock price.
Below is a Python code to calculate PutCall Parity and assess its validity for a given set of parameters:
It calculates the PutCall Parity using the formula:
C  e^(rT) * K = P + S
The function then displays the Lefthand side (LHS) and Righthand side (RHS) of the equation, along with the difference between them. It also checks if the difference is close to zero, indicating that PutCall Parity approximately holds.
Here’s the Python code:
Output:
PutCall Parity Calculation: Lefthand side (LHS): Call option price adjusted for present value of strike  99.63523669507855 Righthand side (RHS): Put option price + Stock price  107 Difference between LHS and RHS: 206.63523669507856 PutCall Parity does not hold.
A close to zero value suggests parity holds but in the output above, it shows putcall parity does not hold.
Let us move to options pricing next.
Options pricing involves determining the fair value of an options contract, which gives the holder the right, but not the obligation, to buy (in the case of a call option) or sell (in the case of a put option) the underlying asset at a specified price (strike price) within a specific period of time.
Below you will find the two types of option pricing techniques and the difference between them. These types are:
The intrinsic value of an option is the value that an option would have if it were exercised immediately.
Below you can see how they are calculated.
Intrinsic Value of Call Option = Current Market Price of Underlying Asset  Strike Price Intrinsic Value of Put Option = Strike Price  Current Market Price of Underlying Asset
The time value of an option is the premium that the option buyer pays for the privilege of having the option until expiration. It reflects the probability that the option will end up inthemoney by expiration.
Time Value = Option Premium  Intrinsic Value
Going forward, we will learn about the options pricing models.
Options pricing models are mathematical models used to determine the fair value of options. Below you will find the different options pricing models and the key differences between each.
Aspect 
DermanKani Model 

Introduction 
Introduced in 1973 by Fischer Black and Myron Scholes 
Proposed by Emanuel Derman and Iraj Kani in 1994 
Developed by Steven Heston in 1993 
Dynamics 
Assumes constant volatility and riskfree interest rate 
Allows for stochastic volatility and stochastic interest rates 
Incorporates stochastic volatility and meanreverting dynamics 
Key Features 
Closedform solution, widely used in finance 
Captures volatility smile, more realistic representation of market conditions 
Captures volatility smile, meanreverting volatility, flexible and realistic 
Model Complexity 
Relatively simple model 
More complex than BlackScholes, but simpler than Heston 
More complex than BlackScholes and DermanKani 
Application 
Suitable for European options on stocks with constant volatility 
Suitable for a wider range of options, including exotic options 
Widely used for pricing options on equities, indices, and currencies 
Limitations 
Assumes constant volatility, doesn't capture volatility smile 
Doesn't capture all market dynamics, requires calibration 
Calibration can be complex and timeconsuming, computationally intensive 
Example 
European call option on a stock 
Options on currencies, interest rates, and commodities 
Options on equities, indices, and currencies 
Each model has its advantages and limitations, and the choice of model depends on the specific requirements of the trader or investor.
Let us now see one of the most popular advanced options’ strategies which is the butterfly strategy and its payoff diagram.
To get to the butterfly strategy’s payoff diagram you need to follow this procedure:
After learning this strategy, you will be able to plot the payoff diagram of any option strategy you might want to set up.
The steps are as follows:
Output:
futures_close Expiry Date 20220520 16253.25 20220526 20220523 16183.35 20220526 20220524 16104.70 20220526 20220525 16013.80 20220526 20220526 16159.05 20220526
Output:
'The futures price on 20210101 is 14053.85'
Output:
Symbol  Expiry  Option Type  Strike Price  Open  High  Low  Close  Last  Settle Price  Number of Contracts  Turnover  Premium Turnover  Open Interest  Change in OI  Underlying  

Date  
20210101  NIFTY  28012021  CE  12000  2017.10  2062.25  2014.0  2043.60  2042.00  2043.60  256.0  269606000.0  39206000.0  456225.0  10200.0  14018.5 
20210101  NIFTY  28012021  CE  12050  0.00  0.00  0.0  609.75  0.00  2009.45  0.0  0.0  0.0  0.0  0.0  14018.5 
20210101  NIFTY  28012021  CE  12100  1923.15  1936.45  1922.6  1934.75  1934.75  1960.25  4.0  4209000.0  579000.0  15750.0  0.0  14018.5 
20210101  NIFTY  28012021  CE  12150  0.00  0.00  0.0  569.95  0.00  1911.10  0.0  0.0  0.0  0.0  0.0  14018.5 
20210101  NIFTY  28012021  CE  12200  0.00  0.00  0.0  1797.80  1799.00  1862.15  0.0  0.0  0.0  22575.0  0.0  14018.5 
Output:
Option Type  Strike Price  position  premium  

0  CE  14050  1  280.75 
1  PE  14050  1  279.00 
2  CE  14600  1  69.25 
3  PE  13500  1  103.00 
Since we have set up the long butterfly strategy, now let's compute the payoff for call and put options.
Remember, that the payoff of a long call option is given by:
Long Call Payoff=𝑀𝑎𝑥(Spot Price−Strike Price,0)−Premium
The Max function is interpreted as the following:
Can you guess how to compute the short call? It's simple, you just need to multiply the above functions by 1 to have the shortsell version of the call option payoff.
Define the call payoff function
Output:
980
Output:
 980
Then, similarly, we can define the put option payoff.
For a long put option payoff, we have the following formula and its interpretation:
Long Put Payoff = 𝑀𝑎𝑥(Strike Price−Spot Price,0)−Premium
Output:
20
Finally, the short put payoff value:
Output:
20
Let's take an example. Let's call the get_payoff function for a specific price and see what the value will be at expiry.
Output:
162.5
Output:
66 15300 67 15350 68 15400 69 15450 70 15500 Name: price_range, dtype: int64
Output:
66 162.5 67 162.5 68 162.5 69 162.5 70 162.5 Name: pnl, dtype: float64
Output:
Output:
'The maximum profit is 387.5 and its corresponding futures price is 14050'
Hence, if the futures price at expiry is 14050, you can expect a maximum profit of 387.5 rupees with the strategy.
Output:
'The maximum loss is 162.5'
Output:
Option Type  Strike Price  position  premium  

0  CE  14050  1  280.75 
1  PE  14050  1  279.00 
2  CE  14600  1  69.25 
3  PE  13500  1  103.00 
Output:
As you can see, the payoff diagram lets us visually understand when we will be getting maximum return with a long or short butterfly strategy. This code above can be used for any strategy payoff you want to obtain.
You can check the entire strategy and more on Butterfly strategy with the course on Systematic Options Trading. This course will also help you learn to backtest options trading strategies and the related concepts in detail.
It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.
Now, we will see how to perform risk management in advanced options trading.
Risk management is crucial in advanced options trading to protect your capital and optimise your returns.
Here are some key risk management strategies for advanced options trading:
By implementing these risk management strategies, you can minimise your downside risk while maximising your potential returns in advanced options trading.
Last, but not least, we will see the resources available for learning options trading.
Learners who are aware of options trading and implementing options trading strategies can start by expanding their knowledge with this list of reads and projects on options trading.
We have curated a list of some of our most demanded blogs on Options Trading written by experts! Do check them out!
Below are the questions that options traders usually ask. So, we have provided the answer to each ahead.
Q: What are the main factors influencing options pricing in advanced trading?
A: Options pricing in advanced trading is influenced by several factors:
Q: How do I choose the right options contract for advanced trading?
A: Choosing the right options contract involves considering several factors:
Q: What role does implied volatility play in advanced options trading?
A: Implied volatility is a critical factor in options pricing and advanced options trading:
Q: What are some common mistakes to avoid in advanced options trading?
A: Common mistakes to avoid in advanced options trading include:
Q: How do I stay updated on market developments relevant to advanced options trading?
A: You can stay updated on market developments by:
Q: Can I use advanced options trading strategies in different market conditions?
A: Yes, advanced options trading strategies can be used in various market conditions:
Advanced options trading offers a vast array of strategies and tools for investors looking to manage risk effectively. Understanding options Greeks, that is, Delta, Gamma, Vega, and Theta is crucial, as they directly impact options pricing and portfolio management.
Volatility strategies are quite essential for success in advanced options trading, and mastering the skills required for implementing these strategies is key.
Knowing how options are priced, the factors influencing pricing, and the various options pricing models are fundamental. Risk management is paramount, and learning how to effectively analyse options Greeks and avoid common mistakes is essential for success. Staying updated on market developments and utilising available resources, such as advanced options trading courses and books, is vital for continuous learning and improvement.
By following the right approach and utilising the right broker, traders can navigate the world of advanced options trading with confidence and competence.
To learn more about advanced options trading, our learning track on Quantitative Trading in Futures and Options Markets covers a bundle of 7 courses to start using quantitative techniques in futures & options trading. With these courses, you will learn volatility forecasting, options backtesting, risk management, option pricing models, greeks, and various strategies such as straddle, butterfly, iron condor, spread strategies, dispersion trading, sentiment trading, box strategy, diversified futures trading strategies and much more.
Files in the download:
Author: Chainika Thakar and Rekhit Pachanekar
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>However, in reality, volatility tends to vary and is seldom constant. Steven Heston developed a mathematical model where volatility is unpredictable and follows a random pattern. Moreover, Heston's model offers a straightforward solution, streamlining the process and gaining wider acceptance in the financial community.
Whether you're a financial analyst, a quantitative researcher, or someone interested in learning about the sophisticated financial models for trading related or work related purposes, this blog will help you grasp the fundamentals of the Heston model. You'll learn about its theoretical underpinnings and gain practical insights into the Heston model and its applications in option pricing.
Let's proceed to explore the topics covered in this blog.
The Heston model, introduced by Steven Heston in 1993, is a mathematical model used in financial mathematics to price options. It is an extension of the BlackScholes model and is widely used to value options where the underlying asset's volatility is not constant but follows a stochastic process.
Volatility represents the magnitude of upward and downward movements in a security over a given period. Technically, it is measured as the standard deviation of the annualised returns over that period, or simply as the square root of the variance of the returns.
In the Heston model, both the underlying asset's price and its volatility are assumed to follow stochastic differential equations (SDEs). The model assumes that volatility follows a meanreverting process, which means it tends to revert to a longterm average over time.
This feature of the model allows it to capture the volatility smile observed in the market, where options with different strike prices but the same maturity may have different implied volatilities. The Heston model has become a standard model for pricing options in both equity and foreign exchange markets due to its ability to capture the dynamics of asset prices and the volatility surface accurately.
Let's first explore why it's important not to treat volatility as a constant. Imagine you maintain volatility as a constant value. Now, if you were to plot a graph with strike prices on the xaxis and the implied volatility of a group of options on the yaxis, you would observe a curved line. This phenomenon is known as the volatility smile.
The reason behind the volatility smile is that implied volatility tends to be higher for deep outofthemoney options and generally decreases as we move towards inthemoney or atthemoney options. Interestingly, the volatility smile was considered rare before the 1987 crash. However, after the crash, traders realised that outofthemoney options, although rare, could occur.
Here is an example of how the graph might look:
According to the BlackScholes model, this line should have been flat. However, to ensure that option prices better reflect realworld conditions, the Heston model introduced a stochastic volatility model. ⁽¹⁾
In the Heston model, two functions are considered:
Going forward, we will understand the general parameters taken into consideration with the Heston model.
The Heston model has several parameters that describe the dynamics of the underlying asset's price and volatility.
The main parameters of the Heston model are:
These parameters are used to define the stochastic differential equations governing the dynamics of the asset price and its volatility in the Heston model.
Let us now see the essentials of the Heston model while pricing the options.
The Heston Model is a mathematical model used to price options. The stochastic differential equations (SDEs) are the essential concepts for the Heston Model. Below you can see both the equations.
dS(t) = µS(t)dt + √v(t)S(t)dW₁(t)
This equation describes the logarithmic price movement of the underlying asset. Here's a breakdown of the terms:
This equation captures the price movement of the asset, considering both the expected return and random fluctuations influenced by volatility.
It is like a miniformula that captures how the price of an asset changes over brief moments in time (represented by dt). It considers two main factors:
By putting these two factors together, this equation allows us to model the price movement of the asset over time considering both the expected trend and the random fluctuations along the way.
2. The second equation represents Volatility Dynamics and is as follows:
dv(t) = κ(θ  v(t))dt + συ(t)dW2(t)
Here's a breakdown of the terms:
This equation models the volatility itself as a separate process with its own mean reversion and random fluctuations.
Volatility, which reflects how much the price fluctuates, isn't always constant. It can rise and fall over time. This equation helps us understand these changes.
Here's what each part signifies:
In essence, this equation allows us to model how volatility itself might change over time. It considers the tendency to revert to a longterm average but also acknowledges the possibility of random ups and downs in volatility.
Both these equations are typically used within the Heston Model. By solving these equations numerically, we can simulate the potential price paths of the underlying asset and its volatility, allowing for more accurate option valuation compared to models with constant volatility.
Let us see the Python code that will generate two plots:
Output:
Output:
Ahead, we will see the steps of the Heston model for pricing European options.
Below are the steps of options pricing using the Heston model. We are taking European call and put options in this example.
Define the parameters of the Heston model that we discussed above.
Use the Heston model characteristic function formula to calculate the characteristic function of the Heston model. The characteristic function is a concept that is widely used in option pricing models like the Heston model.
In the context of the Heston model, the characteristic function is a mathematical function that fully describes the joint distribution of the underlying asset price and its stochastic volatility at expiration.
The characteristic function for the Heston model is given by:
$$\phi(u\;, S_0\;,K\;,r\;,T\;,k\;,θ\;,σ\;,ρ\;,v_0) = exp(C(u\;, S_0\;,K\;,r\;,T\;,k\;,θ\;,σ\;,ρ\;,v_0) + D((u\;, S_0\;,K\;,r\;,T\;,k\;,θ\;,σ\;,ρ\;,v_0)v_0 + iu\;log(S_0))$$ $$where:\\ \bullet u\;is\;the\;integration\;variable\\ \bullet S_0\;is\;the\;initial\;stock\;price\\ \bullet K\;is\;the\;strike\;price\\ \bullet r\;is\;the\;riskfree\;interest\;rate\\ \bullet T\;is\;the\;time\;to\;maturity\\ \bullet k\;is\;the\;mean\;reversion\;rate\\ \bullet θ\;is\;the\;longterm\;average\;volatility\\ \bullet σ\;is\;the\;volatility\\ \bullet ρ\;is\;the\;correlation\;coefficient\;between\;the\;asset\;price\;and\;its\;volatility\\ \bullet v_o\;is\;the\;initial\;volatility$$Use Fourier inversion to compute the option price. Fourier inversion is a mathematical technique used to compute option prices in models like the Heston model. In the context of the Heston model, the characteristic function is used to price options via Fourier inversion.
Fourier inversion involves integrating the characteristic function over a range of frequencies (or a range of values for the integration variable u) to obtain the option price.
For a European call option, the option price can be expressed as:
$$ C = e^{rT} \left( \frac{1}{2}S_0  \frac{1}{\pi} \int_{0}^{\infty} \frac{e^{iu\ln(K)}\phi(u)}{iu}du \right)\\ where\; \phi(u)\; is\;the\;characteristic\;function\;of\;the\;Heston\;model. $$Similarly, for a European put option, the option price can be expressed as:
$$ P = e^{rT} \left( \frac{1}{\pi} \int_{0}^{\infty} \frac{e^{iu\ln(K)}\phi(u)}{iu}\,du \right)  S_0 + Ke^{rT} $$where:
$$ C: \text{European call option price} \\ P: \text{European put option price} \\ S_0: \text{Initial stock price} \\ K: \text{Strike price} \\ r: \text{Riskfree rate} \\ T: \text{Time to maturity} \\ \phi(u): \text{Characteristic function of the Heston model} \\ \int_{0}^{\infty}: \text{Integral from 0 to infinity} \\ e^{iu\ln(K)}: \text{Exponential term in the integrand} \\ du: \text{Integration variable} \\ \pi: \text{Pi, approximately equal to } 3.14159 $$Now we will see the Python implementation for pricing options using the Heston model.
Below is the Python implementation for pricing options using the Heston model. Here are the steps involved in the same: ⁽¹⁾
Output:
European Call Option Price: 27.63 European Put Option Price: 15.06
Let us move to learning about the difference between the Heston model and the BlackScholes model now.
Let us first see how the Heston model differs from the BlackScholes model since Heston is an improvement of the BlackScholes model. ⁽²⁾
Here is a clear distinction in the table below mentioning characteristics of each model.
Aspect 
BlackScholes Model 
Heston Model 
Purpose 
Assumes constant volatility and lognormal distribution of asset returns. 
Explicitly models stochastic volatility, allowing for changes in volatility over time. 
Volatility Dynamics 
There is a fixed volatility throughout. 
It models stochastic volatility as a meanreverting process. 
Parameters 
Considers factors such as current price, time, interest rate, and a fixed volatility. 
Needs more information such as how volatile markets usually are, how fast they go back to normal, and how related price changes are to volatility changes 
Closedform Solution 
Provides closedform solution. 
Doesn't provide a closedform solution. 
Flexibility 
Only works for both basic options and exotic options. Although, it may require extensions or modifications. 
Can handle many types of options, even the exotic options such as barrier, binary etc. 
Adjusting or calibrating difficulty 
Calibrating the BlackScholes model typically involves straightforward adjustments to its input parameters. 
Refining the Heston model to accurately reflect real market dynamics requires a more intricate process, often necessitating iterative adjustments and computational analysis to align the model's parameters with observed market data. 
Let us now move forward and find out the various assumptions of the Heston model.
When using the Heston model, several assumptions are made:
However, it's important to note that in reality, some of these assumptions may not hold true, and adjustments may be necessary when applying the model to realworld situations.
Let us find out the benefits of using the Heston model next.
Using the Heston model offers several benefits:
After seeing the benefits that the Heston model’s use offers, we will now move to the limitations of the same.
The following can be considered as the limitations of the Heston model:
The extensions of the Heston model come next.
Several extensions of the Heston model have been proposed to address its limitations and to better capture the complexities of financial markets. Some of the notable extensions include:
These extensions of the Heston model address some of its limitations and make it a more powerful tool for pricing and hedging a wide range of financial derivatives in realworld market conditions.
The Heston model, an extension of the BlackScholes model, revolutionised options pricing by incorporating stochastic volatility, thus addressing the limitations of its predecessor. By allowing volatility to fluctuate over time, the Heston model accurately captures the volatility smile observed in financial markets. Steven Heston's mathematical model provides a closedform solution, simplifying the pricing process and gaining widespread acceptance.
With this comprehensive guide we explored the intricacies of the Heston model, from its formula and assumptions to its limitations and practical implementation. Through Python examples, we gained a deeper understanding of the model's application in options pricing.
Despite its benefits, the Heston model requires careful parameter calibration and may struggle with shortterm option pricing. However, extensions such as stochastic interest rates and jump diffusion address these limitations, making the Heston model a powerful tool for pricing and hedging financial derivatives in realworld market conditions.
Apart from the Heston Model, other option pricing models are BSM and DermanKani Model, and you may explore them to understand them better in our comprehensive learning track that will help you learn about quantitative trading in the futures and options markets. Grasp this opportunity to learn volatility forecasting, options backtesting, risk management, option pricing models and greeks as well as various trading strategies in a handson manner. Let this be your guide ahead. Enroll now!
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Author: Chainika Thakar (Originally written by Rekhit Pachanekar)
Note: The original post has been revamped on 21^{st} February 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>At its core, the Kalman filter combines information from a series of measurements with predictions from a dynamic model to produce optimal estimates of the system's state. It does so by recursively updating its estimate based on new measurements, while also taking into account the uncertainty associated with both the measurements and the model predictions.
This blog covers:
Imagine the Kalman filter as a useful conductor leading an orchestra of data. What is the use of it? ⁽¹⁾
The use would be to seamlessly merge noisy measurements with predictive models and craft an estimation of a system's state. This blend of past observations and dynamic forecasts is the secret, empowering traders to sail through the uncertainty in the markets with confidence.
Next, we will talk about the applications of the Kalman filter in the trading domain.
Below are some useful applications of the Kalman filter in trading.
Now, let us move ahead to find out the real world examples of usage of the Kalman filter.
One quite interesting real world example of Kalman filter usage is depicted in an article by Bayes Business School in the United Kingdom. An event was held in the school in 2020 led by Dr Veronika Lunina, Quantitative Vice President at NatWest Markets.
In this event, Dr Veronika spoke about the use of the Kalman filter and was positive about her own experiences using the extended Kalman filter for automated marking of FX implied volatility surface.
According to a research paper, Nkomo et al. (2013) introduced the Kalman filter to process stock price data and proposed the KACM algorithm based on the Kalman filter, leveraging momentum effects to expand the AC algorithm and obtained superior excess returns in strategy simulation compared to the AC algorithm.
Jin et al. (2013) initially combined the traditional autoregressive (AR) model with the Kalman filter to obtain improved predictive performance over a single AR model and a single Kalman filter. They further combined the support vector regression (SVR) with the UKF into a new model, with SVR used to address parameter selection issues in the UKF. ⁽²⁾
As such, the Kalman filter can be considered a heavy topic when it comes to the use of maths and statistics. Thus, we will go through a few terms before we dig into the equations. Feel free to skip this section and head directly to the equations if you wish.
Kalman Filter uses the concept of a normal distribution in its equation to give us an idea about the accuracy of the estimate. Let us step back a little and understand how we get a normal distribution of a variable.
Let us suppose we have a football team of ten people who are playing the nationals. As part of a standard health checkup, we measure their weights. The weights of the players are given below.
Player Number 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Weight 
72 
75 
76 
69 
65 
71 
70 
74 
76 
72 
Now if we calculate the average weight, ie the mean, we get the value as (Total of all player weights) / (Total no. of players)
= 720/10 = 72
The mean is usually denoted by the Greek alphabet μ. If we consider the weights as w1, w2 respectively and the total number of players as N, we can write it as: μ = (w1 + w2+ w3+ w4+.....+ wn)/N
Or
$$\mu = \frac{1}{N}\sum_{i=1}^n W_i$$Now, on a hunch, we decide on seeing how much each player’s weight varies from the mean. This can be easily calculated by subtracting the individual’s weight from the mean value.
Now, the first team player’s weight varies in the following manner,
(Individual player’s weight)  (Mean value) = 72  72 = 0.
Similarly, the second player’s weight varies by the following: 75  72 = 3.
Let’s update the table now.
Player Number 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Weight 
72 
75 
76 
69 
65 
71 
70 
74 
76 
72 
Difference from mean 
0 
3 
4 
3 
7 
1 
2 
2 
4 
0 
Now, we want to see how much the entire team’s weights vary from the mean. A simple addition of the entire team’s weight difference from the mean would be 0 as shown below.
Thus, we square each individual’s weight difference and find the average. Squaring is done to eliminate the negative sign of a score + penalise greater divergence from the mean.
The updated table is as follows:
Player Number 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Weight 
72 
75 
76 
69 
65 
71 
70 
74 
76 
72 
Difference from mean 
0 
3 
4 
3 
7 
1 
2 
2 
4 
0 
Squared difference from the mean 
0 
9 
16 
9 
49 
1 
4 
4 
16 
0 
Now if we take the average, we get the equation as,
$$\frac{1}{N}\sum_{i=1}^n (W_i  \mu)^2 = 10.8$$The variance tells us how much the weights have been spread. Since the variance is the average of the squares, we will take the square root of the variance to give us a better idea of the distribution of weights. We call this term the standard deviation and denote it by σ.
Thus,
$$σ = \sqrt\frac{1}{N}\sum_{i=1}^n (W_i  \mu)^2 = \sqrt10.8 = 3.46$$Since standard deviation is denoted by σ, the variance is denoted by σ2.
But why do we need standard deviation?
While we calculated the variance and standard deviation of one football team, maybe we could find for all the football teams in the tournament, or if we are more ambitious, we can do the same for all the football teams in the world. That would be a large dataset.
One thing to understand is that for a small dataset we used all the values, i.e. the entire population to compute the values. However, if it is a large dataset, we usually take a sample at random from the entire population and find the estimated values.
In this case, we replace N by (N1) to get the most accurate answer as per Bessel's correction. Of course, this introduces some errors, but we will ignore it for now.
Thus, the updated equation is,
$$σ = \sqrt\frac{1}{N1}\sum_{i=1}^n (W_i  \mu)^2$$Now, looking at different research conducted in the past, it was found that given a large dataset, most of the data was concentrated around the mean, with 68% of the entire data variables coming within one standard deviation from the mean.
This means that if we had data about millions of football players, and we got the same standard deviation and variance which we received now, we would say that the probability that the player’s weight is +3.46 from 72 kg is 68.26%. This means that 68.26% of the players’ weights would be from 68.53 kg to 75.46.
Of course, for this to be right, the data should be random.
Let’s draw a graph to understand this further. This is just a reference of how the distribution will look if we had the weights of 100 people with mean as 72 and standard deviation as 3.46.
This shows how the weights are concentrated around the mean and taper off towards the extremes. If we create a curve, you will find that it is shaped like a bell and thus we call it a bell curve. The normal distribution of the weights with mean as 72 and standard deviation as 3.46 will look similar to the following diagram.
Normal distribution is also called a probability density function. While the derivation is quite lengthy, we have certain observations regarding the probability density function.
The probability density function is given as follows,
$$f(w,\;\mu,\;σ^2) = \frac{e^\frac{(w\mu)}{2σ^2}}{2\piσ^2}$$The reason we talked about normal distribution is that it forms an important part in Kalman filters.
Let’s now move on to the Kalman filter equations.
Kalman Filter is a type of prediction algorithm. Thus, the Kalman filter’s success depends on our estimated values and its variance from the actual values. In the Kalman filter, we assume that depending on the previous state, we can predict the next state.
At the outset, we would like to clarify that this Kalman Filter tutorial is not about the derivation of the equations but trying to explain how the equations help us in estimating or predicting a value.
Now, as we said earlier, we are trying to predict the value of something which cannot be directly measured. Thus, there will obviously be some error in the predicted value and the actual value.
Kalman Filter is used to reduce these errors and successfully predict the next state.
Now, suppose we pick out one player and weigh that individual 10 times, we might get different values due to some measurement errors.
Mr. Rudolf Kalman developed the status update equation taking into account three values, i.e.
The status update equation is as follows:
Current state estimated value
= Predicted value of current state + Kalman Gain * ( measured value  predicted value of the state)
Let us understand this equation further.
In our example, we can say that given the measured values of all ten measurements, we will take the average of the values to estimate the true value.
To work this equation, we take one measurement which becomes the measured value. In the initial step, we guess the predicted value.
Now since the average is computed, in this example, the Kalman gain would be (1/N) as with each successive iteration, the second part of the equation would be decreasing, thus giving us a betterestimated value.
We should note that the current estimated value becomes the predicted value of the current state in the next iteration.
For now, we know that the actual weight is constant, and hence it was easy to predict the estimated value. But what if we had to take into account that the state of the system (which was the weight in this case) changes?
For that, we will now move on to the next equation in the Kalman Filter tutorial i.e. State extrapolation.
The state extrapolation system helps us to find the relation between the current state and the next state i.e. predict the next state of the system.
Until now, we understood that the Kalman filter is recursive in nature and uses the previous values to predict the next value in a system. While we can easily give the formula and be done with it, we want to understand exactly why it is used. In that respect, we will take another example to illustrate the state extrapolation equation.
Now, let’s take the example of a company trying to develop a robotic bike. If you think about it, when someone is riding a bike, they have to balance the bike, control the accelerator, turn etc.
Let’s say that we have a straight road and we have to control the bike’s velocity. For this, we would have to know the bike’s position. As a simple case, we measure the wheels’ rotation to predict how much the bike has moved. We remember that the distance travelled by an object is equal to the velocity of the object multiplied by the time travelled.
Now, Let’s suppose we measure the rotation at a certain instant of time, ie Δt.
If we say that the bike has a constant velocity v, then we can say the following:
The predicted position of the bike is equal to the current estimated position of the bike + the distance covered by the bike in time Δt.
Here the distance covered by the bike will be the result of Δt multiplied by the velocity of the bike.
Suppose that the velocity is kept constant at 2 m/s. And the time Δt is 5 seconds. That means the bike moves 10 metres between every successive measurement.
But what if we check the next time and find out the bike moved 12 metres? This gives us an error of 2 metres. This could mean two things,
We try to find out how to minimise this error by having different gains to apply to the state update equation.
Now, we will introduce a new concept to the Kalman filter tutorial, i.e. the α  β filter.
Now, if we recall the status update equation, it was given as,
Current state estimated value
= Predicted value of current state + Kalman Gain * ( measured value  predicted value of the state)
We will say that α is used to reduce the error in the measurement, and thus it will be used to predict the value of the position of the object.
Now if we keep the α in place of the Kalman gain, you can deduce that a high value of α gives more importance to the measured value and a low level of α gives less weightage to the measured value. In this way, we can reduce the error while predicting the position.
Now, if we assume that the bike is moving with different velocities, we would have to use another equation to compute the velocity and which in turn would lead to a better prediction to the position of the bike. Here we use β in place of Kalman gain to estimate the velocity of the bike.
We tried to see the relation of how α and β impact the predicted value. But how do we know for sure the correct value of α and β in order to get the predicted value closer to the actual value?
Let us move on to the next equation in the Kalman filter tutorial, i.e. the Kalman Gain equation.
Recall that we talked about the normal distribution in the initial part of this blog. Now, we can say that the errors, whether measurement or process, are random and normally distributed in nature. In fact, taking it further, there is a higher chance that the estimated values will be within one standard deviation from the actual value.
Now, Kalman gain is a term which talks about the uncertainty of the error in the estimate. Put simply, we denote ρ as the estimated uncertainty.
Since we use σ as the standard deviation, we would denote the variance of the measurement σ2 due to the uncertainty as ⋎.
Thus, we can write the Kalman Gain as,
(Uncertainty in estimate)
(Uncertainty in estimate + Uncertainty in measurement)
(Uncertainty in estimate)(Uncertainty in estimate + Uncertainty in measurement)
In the Kalman filter, the Kalman gain can be used to change the estimate depending on the estimated measure.
Since we saw the computation of the Kalman gain, in the next equation we will understand how to update the estimated uncertainty.
Before we move to the next equation in the Kalman filter tutorial, we will see the concepts we have gone through so far. We first looked at the state update equation which is the main equation of the Kalman filter.
We further understood how we extrapolate the current estimated value to the predicted value which becomes the current estimate in the next step. The third equation is the Kalman gain equation which tells us how the uncertainty in the error plays a role in calculating the Kalman gain.
Now we will see how we update the Kalman gain in the Kalman filter equation.
Let’s move on to the fourth equation in the Kalman filter tutorial.
In the Kalman Filter tutorial, we saw that the Kalman gain was dependent on the uncertainty in the estimation. Now, as we know with every successive step, the Kalman Filter continuously updates the predicted value so that we get the estimated value as close to the actual value of a variable, thus, we have to see how this uncertainty in the error can be reduced.
While the derivation of the equation is lengthy, we are only concerned about the equation.
Thus, the estimate uncertainty update equation tells us that the estimated uncertainty of the current state varies from the previous estimate uncertainty by the factor of (1  Kalman gain). We can also call this the covariance update equation.
This brings us to the last equation of the Kalman filter tutorial, which we will see below.
The reason why the Kalman filter is popular is because it continuously updates its state depending on the predicted and measured current value. Recall that in the second equation, we had extrapolated the state of the estimate. Similarly, the estimated uncertainty of the current error is used to predict the uncertainty of the error in the next state.
Ok. That was simple!
This was a no equation way to describe the Kalman filter. If you are confused, let us go through the process and see what we have learned so far.
For input, we have measured value. Initially, we use certain parameters for the Kalman gain as well as the predicted value. We will also make a note of the estimated uncertainty.
Now we use the Kalman filter equation to find the next predicted value.
In the next iteration, depending on how accurate our predicted variable was, we make changes to the uncertainty estimate which in turn would modify our Kalman gain.
Thus, we get a new predicted value which will be used as our current estimate in the next phase.
In this way, with each step, we would get closer to predicting the actual value with a reasonable amount of success.
That is all there is to it. We would reiterate in this Kalman filter tutorial that the reason the Kalman filter is popular is because it only needs the previous value as input and depending on the uncertainty in the measurement, the resulting value is predicted.
In the real world, the Kalman filter is used by implementing matrix operations as the complexity increases when we take realworld situations. If you are interested in the maths part of the Kalman filter, you can go through this resource to find many examples illustrating the individual equations of the Kalman filter.
Moving forward, we will see the comparison of Kalman filter with other filtering techniques to make the topic more clear.
Let us dive into the differences between Kalman filtering and other filtering techniques on the basis of advantages, disadvantages and applicability of each technique. ⁽³⁾
Filtering Technique 
Advantages 
Disadvantages 
Applicability 
Kalman Filter 
Optimal under Gaussian noise assumptions. Efficient for linear systems. Provides estimates of state and error covariance. 
Assumes linearity and Gaussian noise, which may not hold in all cases. Can be computationally expensive for highdimensional systems. 
Tracking moving averages in trading algorithms. Predicting future price movements based on historical data. 
Extended Kalman Filter (EKF) 
Allows for nonlinear system models by linearizing them via Taylor series expansion. More flexible than the standard Kalman filter. 
Linearization introduces approximation errors, leading to suboptimal performance in highly nonlinear systems. May suffer from divergence issues if the linearization is inaccurate. 
Modelling complex trading strategies involving nonlinear relationships between market variables. 
Unscented Kalman Filter (UKF) 
Avoids linearization by propagating a set of sigma points through the nonlinear functions. More accurate than EKF for highly nonlinear systems. Better performance with nonGaussian noise. 
Requires tuning parameters for the selection of sigma points, which can be challenging. May suffer from sigma point degeneracy in highdimensional spaces. 
Estimating the state of a financial market model with highly nonlinear dynamics. 
Particle Filter (Sequential Monte Carlo) 
Handles nonlinear and nonGaussian systems without requiring linearisation. Robust to multimodal distributions. Can represent complex distributions with particles. 
Computational complexity increases with the number of particles, making it less efficient for highdimensional state spaces. Sampling inefficiency can lead to particle degeneracy and sample impoverishment. 
Tracking multiple potential market scenarios simultaneously, such as predicting the movement of various assets in a portfolio. 
Complementary Filter 
Simple to implement and computationally efficient. Effective for fusing data from multiple sensors with complementary characteristics. 
Requires manual tuning of sensor fusion parameters, which may not be optimal in all situations. Limited applicability to systems with highly correlated sensor errors. 
Combining technical indicators, such as moving averages and momentum oscillators, to generate trading signals. 
When it comes to trading, the Kalman filter forms an important component in the pairs trading strategy. Let us build a simple pairs trading strategy using the Kalman Filter in Python now.
Implementing a Kalman filter in Python involves several steps.
Here's a basic guide to the steps used:
Output:
Here's what each component of the plot represents:
The plot allows you to visualise how well the Kalman filter is able to estimate the true state despite the presence of noise in the measurements.
Ideally, the estimated state should closely track the true state, providing a smooth and accurate representation of the underlying system dynamics.
Next, we will see the use of the Kalman filter in the pairs trading strategy where the Kalman filter is mostly used.
(Thanks to Chamundeswari Koppisetti for providing the code.)
Let us start by importing the necessary libraries for the Kalman Filter.
We will consider the 4 years (January 1st, 2020  January 1st, 2024) Adjusted Close price data for Bajaj Auto Limited (BAJAJAUTO.NS) and Hero MotoCorp Limited (HEROMOTOCO.NS).
We have included the data file in the zip file along with the code for you to run on your system later. The link to download the files can be found at the end of the blog.
Output:
Bajaj Hero Ratio Date 20190101 2726.649902 3127.600098 0.871803 20190102 2692.000000 3046.550049 0.883622 20190103 2701.350098 3014.649902 0.896074 20190104 2734.199951 2987.850098 0.915106 20190107 2658.550049 2957.949951 0.898781 ... ... ... ... 20231222 6372.100098 3935.699951 1.619051 20231226 6464.549805 4067.449951 1.589337 20231227 6709.649902 4064.300049 1.650875 20231228 6703.299805 4173.250000 1.606254 20231229 6797.250000 4139.549805 1.642026
Hyperparameters of the Kalman Filter can be changed for instance:
Output:
In the pairs trading strategy, we buy one stock and sell the other stock choosing the quantity as the hedge ratio.
Output:
Total returns: 0.03794040475865804
You can optimise the strategy parameters to get different results.
It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.
Next, let us find out what future trends and developments are in the pipeline for the trading domain using Kalman filter technology.
Here are some potential future trends and developments in Kalman filter technology: ⁽⁴⁾
Overall, Kalman filters are likely to play an increasingly important role in algorithmic trading. By integrating with advanced machine learning techniques, handling more complex data sources, and becoming more interpretable, Kalman filters could provide traders with a powerful tool to navigate the everevolving financial markets.
By mastering statistical concepts and Kalman filter equations, we gained insight into how it optimally combines measurements and predictions to estimate a system's state with precision.
Exploring realworld examples showcased its versatility in pairs trading, volatility estimation, market impact modelling, portfolio optimisation, and algorithmic trading strategies. We delved into practical implementation steps in Python, emphasising efficiency and accuracy through optimised code and performance strategies.
Comparisons with other filtering techniques highlighted its strengths in Gaussian noise environments while envisioning future trends focused on integration with machine learning, multifactor modelling, alternative data sources, cloudbased processing, and explainability.
With these insights, traders are empowered to leverage the Kalman filter effectively, navigating the complexities of financial markets with confidence and adaptability. As we embrace the future of algorithmic trading, the Kalman filter remains a cornerstone, evolving alongside technological advancements to meet the challenges of tomorrow's trading landscape.
You can learn more about the Kalman filter and the statistical concepts such as cointegration, ADF test to identify trading opportunities in order to create trading models using spreadsheets and Python. Happy trading!
Author: Chainika Thakar (Originally written by Rekhit Pachanekar)
Note: The original post has been revamped on 7^{th} May 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>From understanding the fundamentals of portfolio construction to implementing sophisticated risk management techniques, this guide will equip you with the necessary skills to navigate complex financial markets with more confidence! Join us as we delve into the realm of portfolio management strategies with Python and unlock endless possibilities for managing your trading portfolio with Python.
We cover:
Portfolio management involves the strategic allocation and management of assets to achieve specific investment objectives while balancing risk and return. Managing a portfolio or handling multiple strategies doesn't deviate much from managing a portfolio of assets. Here, the operational assets are the strategies themselves. These strategies involve long, short, or waiting positions, all aiming to maximise returns while minimising risks.
The fundamental question arises: How should capital be allocated among various strategies and instruments to optimise returns and mitigate risks?
To establish a benchmark for optimisation, we initially distribute equal weights to each element within a simple portfolio. Numerous academic studies explore optimising capital distribution weights, each focusing on different parameters.
Two prominent and contrasting methods include:
You will find a detailed learning of these two methods mentioned above in the course on Quantitative Portfolio Management. It is necessary that the traders get familiar with these and other methods to determine the most suitable approach aligning with their investment style and risk tolerance.
Let us see the essential concepts of portfolio management next to learn the concept in detail later.
The essential concepts of portfolio management are:
“An efficient portfolio is defined as a portfolio with minimal risk for a given return, or, equivalently, as the portfolio with the highest return for a given level of risk.”
Efficient portfolios are the smartest way to manage your money when you invest. Imagine spreading your money across different types of investments, like shares, bonds, and property. This helps keep your money safe even if the market performs unexpectedly. In an efficient portfolio, as a trader, you will look at things such as predicting the returns from each trade, how risky each trade is, and how they behave compared to each other. It's all about finding the right mix.
Alongside, you've got to keep an eye on the markets and make changes in your trades as and when needed. Markets change, economies shift, so what's good today might not be tomorrow. When we only have one portfolio management strategy managing one instrument, portfolio management is limited to maximising return while minimising risk. This would be the simplest portfolio, but not a simple solution.
It is not a simple solution because we have to answer some questions.
On the other hand, if we want to diversify the portfolio and, therefore, reduce the risk associated with the portfolio management strategy or instrument, we must build a portfolio with different instruments and ideally different strategies that capture different market regimes. Therefore, in addition to the above questions, we need to answer what weight we assign to each portfolio management strategy and what weight we give to each instrument within the portfolio to achieve the required objective (Max return vs Min risk).
We will check the elements of a portfolio next.
Let's define the portfolio's elements below.
By carefully considering and managing these elements, traders can construct portfolios that align with their financial goals, risk tolerance, and investment preferences.
Let us see the performance measures or the various metrics to find out the performance of an ideal portfolio.
Algorithmic traders have at their disposal a large number of measures or performance metrics to analyse the portfolio management strategy and/or the portfolio performance.
Some of the most used portfolio performance metrics are:
In addition to these individual measures, the pyfolio library implements a fantastic catalogue of performance measures and graphics that are certainly worth learning to use. We will see some of their performance reports through this post.
Now, let us move to building a simple portfolio part.
To build our example portfolio we are going to use two methods. One with two stocks and three strategies for portfolio management and the other with three stocks and again three strategies.
It is needless to say any strategy that is considered to be part of the portfolio should undergo backtesting that offers us an adequate level of certainty about the strategy returns. Hence, it is important to learn backtesting if not done yet.
Going forward, let us check the instruments or the assets that are utilised in portfolio management.
Assets are the main elements of a portfolio and their characteristics are decisive for obtaining the determined risk/benefit ratio. Some of the most important assets are:
Next, we will find out the multiple investment strategies deployed in portfolio management.
There are certain investment strategies that can be implemented using various Python libraries such as NumPy, pandas, scipy, and scikitlearn, along with tools for optimisation and simulation. Additionally, financial data can be fetched using APIs like Yahoo Finance or Alpha Vantage for analysis and implementation of these strategies.
Here are multiple portfolio management strategies that can be implemented in Python:
We will see the fundamentals for the portfolio management practice using Python next.
Python offers a robust set of tools and libraries that make it a powerful choice for portfolio management. Here are some fundamental Python concepts and tools essential for portfolio management:
By mastering these Python fundamentals and leveraging the rich ecosystem of libraries and tools available, one can effectively manage portfolios, analyse investment strategies, and make datadriven investment decisions.
Now, let us get to the implementation part. We will implement different strategies with two sets of portfolios. One portfolio with two assets and another one with three assets.
Let us see the examples of the implementation of different strategies in portfolio management with 
The strategies used in this are:
The strategies used in this are:
We have discussed these strategies briefly earlier in this blog.
Visualisation of daily returns and cumulative returns
Let us, first of all, see the visualisation of a portfolio with 2 stocks, that is, APPLE (ticker = AAPL) and Cocacola (ticker = KO). We will see the daily returns as well as the cumulative returns of the portfolio.
Output:
Portfolio Performance Metrics: Sharpe Ratio: 0.90 Average Daily Return: 0.0007 Average Annualised Return: 0.17 Volatility (Standard Deviation of Daily Returns): 0.0121
In the output above, the following are the observations:
Investment strategies using the portfolio of two assets
Let us now visualise the portfolio of two assets, that is, ‘AAPL and KO’ using different strategies namely:
Output:
Here's what each graph above signifies:
Each plotted graph provides insight into how different portfolio construction strategies perform over time, allowing investors to evaluate their effectiveness in achieving investment objectives and managing risk. If the desired results from the strategy are not achieved, the parameters in the portfolio such as weights assigned, volume etc. can be set accordingly.
Using the same strategies, you can include a portfolio of as many assets as you usually trade with having a low or negative correlation with each other.
Including assets with low correlation can help reduce portfolio risk while potentially enhancing returns. The specific assets included in an efficient portfolio depend on various factors such as investment objectives, risk tolerance, time horizon, and market conditions.
This time, we will take into consideration a portfolio with 3 stocks, that is, APPLE (ticker = AAPL), Cocacola (ticker = KO) and Old National Corp (ticker = ONB). We will see the daily returns as well as the cumulative returns of the portfolio.
After this, we will see the portfolio performance using each of the three strategies, namely
In the code below, we have compiled all the steps necessary for the same.
Output:
Each graph in the output above represents a distinct portfolio strategy and its performance:
It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.
From the above output, you can see how a portfolio of three stocks with three different strategies perform. On the basis of your analysis, you can create a portfolio of various stocks and utilise the three strategies as mentioned above.
Going forward, we will see how to do risk management in portfolio construction.
Risk management in portfolio construction is vital for achieving investment goals while minimising potential losses. Diversification, spreading investments across various asset classes, sectors, and regions, mitigates risk by avoiding overexposure to any single asset or market segment. Asset allocation strategically distributes investments based on risk tolerance, aligning the portfolio with the investor's objectives.
Thorough risk assessment identifies and quantifies different types of risks, such as market risk and credit risk, enabling the implementation of appropriate risk management strategies. Regular monitoring of portfolio risk metrics and performance facilitates timely adjustments and rebalancing to maintain the desired risk profile. Overall, effective risk management practices are essential for navigating market uncertainties and safeguarding investment portfolios.
Now we will be seeing the role and importance of quantitative analysis in portfolio management.
Quantitative analysis in portfolio management harnesses mathematical and statistical methods to inform investment decisions. Key aspects include:
Overall, quantitative analysis empowers portfolio managers with datadriven insights to navigate markets efficiently and achieve investment objectives.
Now we will check out which strategies contradict each other in the portfolio management practice.
When you're piecing together a portfolio of different strategies using Python, it's crucial to steer clear of combinations that work against each other, defeating the purpose of diversification. Let's look at a couple of scenarios to avoid:
Picture one strategy that buys stocks whenever a particular momentum indicator goes up and another strategy that sells those same stocks when the same indicator goes down. You'd end up with a lot of activity but not necessarily a lot of overall gain.
Let us now see the future trends in Python for portfolio management and on the basis of what the research says for the same.
Below are the potential future trends in Python for portfolio managers. ⁽¹⁾
Portfolio management, coupled with Python's analytical methods, offers investors a powerful toolkit for navigating financial markets. By emphasising diversification, risk management, and quantitative analysis, investors can construct robust portfolios aligned with their objectives. As Python continues to evolve, its role in portfolio management is poised to expand, driving innovation and efficiency in investment strategies.
With a commitment to harnessing datadriven insights and adapting to emerging trends, investors can confidently navigate the complexities of portfolio management, achieving longterm success in their financial endeavours.
In case you wish to learn about effective portfolio management with Python and quantitative methods in detail, explore our learning track: "Portfolio Management and Position Sizing using Quantitative Methods." Find out the diverse strategies for optimising trade size, capital allocation, and handle the portfolio management challenges headon. Be sure to check it out to transform your portfolio management approach!
File in the download
Author: Chainika Thakar (Originally written by Mario Pisa)
Note: The original post has been revamped on 2^{nd} May 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>In this guide, we delve into Fibonacci retracement levels and their implementation using Python, enabling traders to leverage these mathematical principles for informed decisionmaking.
By combining technical analysis with programming capabilities, traders gain a deeper understanding of market dynamics and enhance their ability to execute trades with maximum returns. So let us dive in and unlock the potential of the Fibonacci Retracement Trading Strategy in Python for navigating volatile financial markets.
Moving ahead, let us find out more with this blog that covers:
The Fibonacci retracement strategy involves the use of the Fibonacci sequence. So, let us first of all learn about the Fibonacci sequence.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. The sequence usually is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.
The sum is in the following order:
In mathematical terms, the Fibonacci sequence can be defined recursively by the formula:
X(n) = X(n1) + X(n2)
Where:
In finance and trading, the Fibonacci sequence is widely used in technical analysis to identify potential support and resistance levels and is an essential part of the Fibonacci retracement strategy.
Moreover, there are some interesting properties of the Fibonacci sequence.
Xn/Xn1 = 1.618
55/34 = 1.618
89/55 = 1.618
144/89 = 1.618
1.618 is known as the golden ratio. I suggest searching for the golden ratio examples on the Google images and you will be pleasantly astonished by the relevance of the ratio in nature.
2. Similarly, divide any number in the sequence by the next number; the ratio is always approximately 0.618.
Xn/Xn+1 = 0.618
34/55 = 0.618
55/89 = 0.618
89/144 = 0.618
3. 0.618 expressed in percentage is 61.8%. The square root of 0.618 is 0.786 (78.6%).
Similar consistency is found when any number in the sequence is divided by a number two places right to it.
Xn/Xn+2 = 0.382
13/34 = 0.382
21/55 = 0.382
34/89 = 0.382
0.382 expressed in percentage is 38.2%
4. Also, there is consistency when any number in the sequence is divided by a number three places right to it.
Xn/Xn+3 = 0.236
21/89 = 0.236
34/144 = 0.236
55/233 = 0.236
0.236 expressed in percentage terms is 23.6%.
5. The ratios 23.6%, 38.2%, 61.8%, and 78.6% are known as the Fibonacci ratios.
Now we can move to learning about Fibonacci retracement strategy.
The Fibonacci retracement strategy is a popular technical analysis tool to identify potential reversal levels in financial markets and is used by traders. Based on the Fibonacci sequence, this strategy involves plotting key retracement levels. The typical or default levels are 23.6%, 38.2%, 50%, 61.8%, and 78.6%, against a price movement.
These levels are derived from ratios found in the Fibonacci sequence, believed to represent areas of support or resistance.
Fibonacci retracement levels help traders to identify the entry and exit points for trades. Hence, the determination of the stoploss and takeprofit levels is done. When the price of an asset retraces to one of these Fibonacci levels, it may indicate a potential reversal in the prevailing trend.
The Fibonacci ratios, 23.6%, 38.2%, and 61.8%, can be applied for time series analysis to find support levels. Whenever the price moves substantially upwards or downwards, it tends to retrace back before it continues moving in the original direction.
For example, if the stock price has moved from $200 to $250, it is likely to retrace to $230 before it continues to move upward. The retracement level of $230 is forecasted using the Fibonacci ratios.
We can arrive at $230 by using simple maths.
Any price below $230 provides a good opportunity for the traders to enter into new positions in the direction of the trend. Likewise, we can calculate for 23.6%, 61.8% and the other Fibonacci ratios.
The Fibonacci retracement strategy is commonly applied alongside other technical indicators and analysis techniques to confirm signals and enhance trading decisions. Additionally, it can be used across various financial instruments and timeframes, making it a versatile tool for traders across different markets.
Let us now find out how to use Fibonacci retracement in trading.
The retracement levels can be used to buy a particular stock but you have not been able to because of a sharp runup in the stock price.
In such a situation, it is recommended to wait for the price to correct to Fibonacci retracement levels such as 23.6%, 38.2%, and 61.8% and then buy the stock. The ratios 38.2% and 61.8% are the most important support levels.
This Fibonacci retracement trading strategy is more effective over a longer time interval and like any indicator, using the strategy with other technical indicators such as RSI, MACD, and candlestick patterns can improve the probability of success.
Now, we will head to calculating Fibonacci retracement levels using Python.
As we now know, retracements are the price movements that go against the original trend. To forecast the Fibonacci retracement level we should first identify the total up move or total down move. To mark the move, we need to pick the most recent high and low on the chart.
Let’s take an example of Exxon Mobil to understand the Fibonacci retracement construction.
Output:
Output:
Minimum Price: 31.56999969482422 Maximum Price: 121.37000274658203
Output:
Level Price 0 121.37000274658203 0.236 100.17720202636718 0.382 87.06640158081055 0.618 65.8736008605957 1 31.56999969482422
It is visible that the maximum price is 121.37 where the level is 0 since there is no retracement at the maximum price.
The first retracement level is at 23.6% is $100.17, the second retracement level is at 38.2% is $87.06, and the next retracement level is at 61.8% is $65.87.
When you implement Python for the Fibonacci trading strategy, there are chances that optimisation will be required to improve the strategy performance.
Consider the following tips and best practices for the same:
By following these tips and best practices, traders can optimise their Fibonacci trading strategy in Python and improve their overall trading performance.
Moving to the next section, we will find out how to overcome the challenges faced while using the Fibonacci trading strategy.
Challenges with the Fibonacci Trading Strategy 
Ways to Overcome the Challenges 
Subjectivity: Identifying the correct swing highs and lows to anchor Fibonacci retracement levels can be subjective and may vary among traders. 
Use Objective Criteria: Define clear criteria for identifying swing highs and lows, such as significant price peaks and troughs, or use automated tools to detect these points. Additionally, consider using multiple timeframes to confirm key levels. 
Overfitting: There is a risk of overfitting the Fibonacci levels to historical data, leading to poor performance in realtime trading. 
Validate with Backtesting: Test the Fibonacci strategy on historical data across different market conditions to ensure robustness. Avoid overoptimising the strategy based on specific past events. Incorporate risk management rules to limit potential losses. 
False Signals: Fibonacci retracement levels may sometimes generate false signals, resulting in poor trade execution and losses. 
Combine with Other Indicators: Use Fibonacci levels in conjunction with other technical indicators, such as moving averages, trendlines, or candlestick patterns, to confirm trade setups. This can help filter out false signals and improve the reliability of the strategy. 
Emotional Bias: Traders may become emotionally attached to Fibonacci levels, leading to biased decisionmaking and reluctance to adapt to changing market conditions. 
Stay Disciplined: Stick to predefined trading rules and objectives, regardless of emotional impulses or attachment to Fibonacci levels. Regularly review and adjust the strategy based on objective performance metrics and market feedback. 
Market Noise: In choppy or volatile market conditions, Fibonacci levels may not accurately capture price movements, resulting in increased noise and false signals. 
Adjust Parameters: Consider adjusting the sensitivity of Fibonacci levels by modifying the anchor points or using alternative Fibonacci tools, such as Fibonacci extensions or clusters, to better align with prevailing market dynamics. Additionally, apply filters to smooth out noise and focus on highprobability trade setups. 
The Fibonacci retracement trading strategy in Python offers traders a systematic approach to navigating volatile financial markets and enables them to unlock the potential for maximum returns.
Mastering the Fibonacci retracement trading strategy in Python equips traders with a powerful tool for identifying potential price reversal levels and making informed trading decisions. By leveraging the Fibonacci sequence and ratios, traders can pinpoint key support and resistance levels, allowing for precise entry and exit points in the market. Through the implementation of Python programming, traders gain the ability to calculate and visualise Fibonacci retracement levels accurately, enhancing their technical analysis capabilities.
If you wish to learn more about the Fibonacci retracement strategy, check out the course on price action trading strategies. This course will help you learn the strategies and codes that help you to tweak, finetune and implement this strategy in the live markets. Learn how to spot and trade the most important trading patterns: double tops/double bottoms, triple tops/triple bottoms, head and shoulders. Get acquainted with several trading strategies, and price action tools such as pivot points and the Fibonacci Retracement levels via a practical approach. Enroll now!
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Author: Chainika Thakar (Originally written by Ishan Shah)
Note: The original post has been revamped on 29^{th} April 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>Join us as we explore a range of esteemed courses and certifications, including the ones that can refine your skillset, while helping you explore the future of finance, that is, algorithmic trading. From industrystandard qualifications to specialised programmes, get ready to equip yourself for the cuttingedge of the financial world.
We cover:
Algorithmic trading, often referred to as algo trading, is the process of using computer algorithms to execute trades in financial markets. These algorithms are programmed to follow predefined instructions, such as price, timing, or quantity, to place trades automatically without human intervention.
Algo trading has become increasingly prevalent in finance due to advancements in technology and the availability of highspeed internet as well as powerful computing systems. It is widely used by institutional investors, hedge funds, and proprietary trading firms to execute large volumes of trades efficiently and quickly.
Let us now find out some common skills that MBA graduates and algorithmic traders can possess.
While MBA programs and algo trading may seem like separate fields, there are several skills common to both that can be leveraged effectively in algo trading:
Nevertheless, the legal considerations and regulatory compliance will be something the MBA graduates will have to learn about separately. Still, the knowledge that the students gain from learning about business related compliance helps to create a base for acquiring further knowledge about algo trading related regulatory compliance.
Moving forward, you must read about some of the success stories of MBA graduates’ transition to algo trading and how they were able to make a very successful career in algo trading. While algo trading is considered to be quite a lucrative career option these success stories can help you understand how individuals from different backgrounds and profiles pursue algo trading after their MBA.
There is a list of success stories of MBA graduates who moved to algo trading by keeping the grit, dedication and an optimistic attitude towards learning and starting a career in algo trading.
To name a few, Srinivas Hosur, a Compliance and Risk Analyst at iRageCapital, has an interesting journey of transitioning to algorithmic trading. One more example is Diego Collaziol, a former Biochemist who turned into a successful Algorithmic Trader and founder of Nuna Muru Investments.
Manuel Roldan is another name who was an Accountant from Venezuela. Despite lacking a computer science background, he pursued Quantra's courses and became a successful algorithmic trader.
Similarly, you can embark on your own path to enrich your understanding of algorithmic trading with the help of Executive Programming in Algorithmic Trading as well as Quantra.
Now the question that arises is, “How can you transition from MBA to Algo Trading?”
Let us find out the steps necessary to transition from MBA to algo trading which must not be missed.
Transitioning from an MBA to a career in algo trading requires careful planning and the acquisition of specific skills and knowledge. Here are the steps you can take to make this transition:
Certifications such as Chartered Financial Analyst (CFA), Financial Risk Manager (FRM), or Certified Quantitative Finance Analyst (CQF) can enhance your credentials and credibility in the field.
By following these steps and continuously learning and adapting to changes in the industry, you can successfully transition from an MBA to a career in algo trading. It requires dedication, continuous learning, and practical experience, but the rewards can be significant for those passionate about quantitative finance and algorithmic trading.
Transitioning to algo trading requires a blend of quantitative, programming, and financial skills. Here are some courses and certifications that can help with this transition:
Networking is crucial for maximising career opportunities post MBA. Proactive networking builds genuine connections, granting access to unadvertised job openings, internships, and projects aligned with career goals.
By showcasing skills at events and online, individuals establish a personal brand, enhancing credibility and visibility. Networking also keeps professionals updated on industry trends, enabling adaptation and positioning for success amidst industry changes.
Embarking on the journey beyond an MBA in Finance opens up a world of possibilities and opportunities for career advancement. Courses and certifications that help to make a career in algorithmic trading offer a pathway to delve into the realm of automated trading strategies, harnessing the power of data analysis and technology to navigate financial markets effectively.
By following a strategic approach, continuously learning, and building a strong professional network, individuals can successfully transition from an MBA to a rewarding career in algo trading, equipped with the knowledge, skills, and connections needed to thrive in dynamic and evolving financial environments.
Don't forget to take a peek at our Quant Jobs page! Once you wrap up your course, the friendly career cell team at QuantInsti doesn't just disappear – they're there to offer you fulltime support, helping all students find their footing in the professional world. And the best part? QuantInsti's 350+ esteemed hiring partners spread out over 20+ countries are on the lookout for top talent, offering secure and highly coveted roles like Quantitative Analyst, Quant Developer, and Risk Manager, just to name a few.
It's a great opportunity for any quant professional. Be sure to check it out now!
Author: Chainika Thakar
Note: The original post has been revamped on 24^{th} April 2024 for recentness, and accuracy.
Disclaimer: All data and information provided in this article are for informational purposes only. QuantInsti^{®} makes no representations as to accuracy, completeness, currentness, suitability, or validity of any information in this article and will not be liable for any errors, omissions, or delays in this information or any losses, injuries, or damages arising from its display or use. All information is provided on an asis basis.
]]>In this guide, we delve into the mechanics of this strategy, exploring its implementation and backtesting results using Python. We'll cover the basics such as the historical context, and the sources driving its returns, as well as the advanced topics such as its comparison with other investment approaches like longonly and marketneutral strategies.
Additionally, we'll address common myths surrounding the strategy and provide stepbystep guidance on building and implementing it effectively. From understanding the ranking scheme and capital allocation to managing risk and transaction costs, this comprehensive guide offers insights into the nuances of longshort equity investing, highlighting its pros and cons.
This blog covers:
The longshort equity strategy involves buying the stocks expected to rise (long positions) and selling the stocks expected to fall (short positions). It aims to gain from both market upswings and downturns while minimising overall market exposure.
An example of a longshort equity strategy involves simultaneously buying shares of undervalued companies (going long) while selling shares of overvalued companies (going short).
For instance, suppose an investor identifies Company A as undervalued and Company B as overvalued based on fundamental analysis. They would buy shares of Company A with the expectation that its stock price will increase (long position) and sell shares of Company B with the anticipation that its stock price will decline (short position).
By maintaining a balanced portfolio of long and short positions, this strategy allows traders to potentially generate returns regardless of whether the broader market is trending up or down.
Let us see some real life examples of undervalued stocks and overvalued stocks which can be included in the long short equity strategy.
In JanMarch 2024, below is the list of overvalued and undervalued stocks.
Company Name  Ticker  Economic Moat  Price/Fair Value Ratio 
Wingstop  Wing  Narrow  2.72 
Celsius  CELH  None  1.85 
Southwest Airlines  LUV  None  1.82 
Vistra  VST  None  1.78 
Dell Technologies  DELL  None  1.77 
Company Name  Ticker  Economic Moat  Price/Fair Value Ratio 
Wingstop  Wing  Narrow  2.72 
Celsius  CELH  None  1.85 
Southwest Airlines  LUV  None  1.82 
Vistra  VST  None  1.78 
Dell Technologies  DELL  None  0.82 
Now, let us see how long short equity strategy came into existence.
The history of long short equity strategy dates back to the 20th century with the rise of the hedge funds since this strategy is most commonly deployed in hedge funds. Let us see below how this strategy came into existence gradually with the milestones mentioned.
20th century  Rise of hedge funds
The history of the longshort equity strategy dates back to the early 20th century when investors began employing techniques to mitigate market risk while capitalising on individual stock movements. However, the strategy gained prominence in the latter half of the 20th century with the rise of hedge funds and institutional investors.
1950s and 1960s  Value investing began
In the 1950s and 1960s, investors such as Benjamin Graham and Warren Buffett popularised value investing, a fundamental principle underlying the longshort equity strategy. They advocated for buying undervalued stocks and short selling overvalued ones to profit from discrepancies in market pricing.
1970s and 1980s  Emergence of long short equity strategies
During the 1970s and 1980s, advancements in financial theory and computing technology facilitated the implementation of more sophisticated quantitative models for stock selection and portfolio management. This period saw the emergence of quantitativelydriven longshort equity strategies, leveraging statistical analysis and mathematical algorithms to identify profitable opportunities.
Late 20th century and early 21st century
In the late 20th and early 21st centuries, regulatory changes, increased competition, and the proliferation of financial instruments further shaped the landscape of longshort equity investing. Today, the strategy continues to evolve with developments in data analytics, machine learning, and artificial intelligence, enabling investors to refine their approaches and adapt to changing market conditions. ⁽²⁾
Next you will see the sources of strategy returns.
The returns generated by a long short equity strategy stem from mainly the following sources:
Now that you understand the basics of long short equity strategy, let us move forward and find out the types of long short equity fund.
Longshort equity funds come in various types, each with distinct characteristics and investment strategies tailored to specific market conditions and investor preferences. A few common and popular types are: ⁽²⁾
Moving forward, we will see the differences between long short equity strategy and longonly investing.
Aspect 
Long Short Equity Strategy 
LongOnly Investing 
Investment Strategy 
Takes both long and short positions in equities, aiming to profit from stock gains and declines. 
Invests only in long positions, expecting stock prices to rise over time. 
Risk Management 
Seeks to minimise market exposure by balancing long and short positions, reducing overall portfolio risk. 
Typically carries higher market risk as it is fully exposed to market movements. 
Profit Potential 
Potentially higher returns due to the ability to profit from both rising and falling stock prices. 
Returns are dependent solely on the performance of long positions, limiting profit potential. 
Diversification 
Offers greater diversification by spreading risk across both long and short positions. 
Limited diversification as it focuses solely on long positions. 
Market Sensitivity 
Less sensitive to overall market movements due to the ability to generate profits in both bullish and bearish markets. 
Highly sensitive to market fluctuations as it lacks the ability to profit from falling stock prices. 
There is a considerable difference between long short equity strategy and market neutral strategy as well which we will see next.
Aspect 
Long Short Equity Strategy 
Market Neutral Strategy 
Investment Strategy 
The primary objective is to generate alpha (excess returns) by selecting individual stocks that are expected to outperform (long positions) and underperform (short positions) the broader market. 
The focus is on generating returns from relative price movements between correlated assets while minimising exposure to broader market movements. It aims for consistent returns regardless of overall market direction. 
Risk Profile 
Typically carries higher risk due to exposure to market fluctuations. It may experience significant drawdowns during market downturns. 
Generally has lower directional risk as it seeks to maintain a neutral market exposure. However, it may still be exposed to specific risks related to the assets being traded. 
Performance 
Has the potential for higher returns, but also comes with higher volatility and potential for losses, especially during turbulent market conditions. 
Typically aims for more consistent, albeit lower, returns with lower volatility. It focuses on generating alpha through relative price movements rather than market direction. 
Market Conditions 
Often performs well in trending markets or during periods of high volatility when there are significant price movements in individual stocks. 
May perform well in more stable market conditions or during periods of low correlation between assets, as it relies on relative price movements. 
There is one more term that is widely used in trading, that is, value investing which also takes into consideration the overvalued and undervalued stocks. Let us find out how long short equity strategy is different from value investing.
Aspect 
Long Short Equity Strategy 
Value Investing 
Investment Approach 
Actively trades both long and short positions in equities based on shortterm price movements and market inefficiencies. 
Takes long positions in undervalued stocks with strong fundamentals, aiming to profit from their potential appreciation over the long term. 
Holding Period 
Typically holds positions for short to medium terms, capitalising on shortterm market fluctuations and mispricing opportunities. 
Often maintains longterm positions, allowing time for undervalued stocks to realise their intrinsic value and deliver returns. 
Risk Management 
Manages risk through a combination of long and short positions, seeking to capitalise on both market upswings and downturns while minimising overall portfolio risk. 
Focuses on mitigating risk through thorough fundamental analysis, selecting stocks with strong fundamentals and margin of safety. 
Profit Potential 
Offers potential for higher returns by actively trading on shortterm price movements and market inefficiencies, but also entails higher risk. 
Typically aims for moderate, consistent returns over the long term, focusing on capital preservation and compounding returns. 
Investment Philosophy 
Emphasises capitalising on market inefficiencies and shortterm price movements to generate alpha, often utilising quantitative models and algorithmic trading strategies. 
Advocates for a patient, disciplined approach to investing, seeking to buy quality stocks at discounted prices and holding them for the long term. 
Going forward, we will see the working of the long short equity strategy.
To understand the workings of this strategy let’s take a look at an example. A hedge fund takes a $1000 long position each in Apple and Google, and a $1000 short position each in Microsoft and IBM.
Portfolio (Technology Sector)
Stock Name 
Long Position 
Stock Name 
Short Position 
Apple 
$1000 
Microsoft 
$1000 

$1000 
IBM 
$1000 
Total 
$2000 
Total 
$2000 
For an event that causes all the stocks in the technology sector to fall, the hedge fund will have losses from long positions in Apple and Google but will have profit from short positions in Microsoft and IBM.
Thus, there will be minimal impact on the portfolio. Similarly, an event that causes all the stocks in the technology sector to rise will also have minimal impact on the portfolio. The hedge fund took this position because they expected Apple and Google’s share prices to rise and Microsoft and IBM’s share prices to fall.
If the view of a fund manager is biased towards the long side, then he can give more weight to the long side of the portfolio such as 70% of the capital to the long side and 30% of the capital to the short side.
However, the impact of the market crash on the portfolio will be higher. But such a construct with a higher proportion in long positions would help the portfolio value to appreciate faster in the bull run, like the one seen after the fall due to COVID19.
There are certain myths surrounding the long short equity strategy that you must know.
Several myths surround the longshort equity strategy, often clouding investors' perceptions. Let us see these myths below.
The steps to building a long short equity strategy will be discussed next.
A long short equity strategy is built with the following steps:
Let's learn about each step in detail and create our own long short equity strategy.
Identify a universe of stocks in which we will take positions. The universe can be defined based on dollarvolume, market capitalisation, price, and impact costs. Here, we will use market capitalisation to identify our stocks.
From the universe of stocks, we will bucket stocks based on the sector such as technology, pharmaceuticals, automobiles, financial services, and FMCG. For our example, we will be using the technology sector.
This is the key step in the workflow. Here we will rank stocks in the bucket based on the previous day’s returns. Stocks that have performed well will be ranked higher and stocks that performed poorly will be ranked lower. We will use the principle of mean reversion to take our trades. We will go long on stocks with the lower rank and go short on the stocks with the higher rank.
Note: A combination of parameters such as quarterly earnings growth, PE ratio, P/BV, moving averages, and RSI could be used here with different weights on each parameter to create a profitable strategy.
Allocating an equal amount of capital to each stock shortlisted from step 3 is a popular capital allocation strategy. An equal weight approach helps to avoid a concentration on a particular stock in the portfolio.
Let us now see the calculation part in the long short equity strategy with Python.
First, let’s start with importing all the necessary libraries. We will be using the yfinance library to import our data. For this strategy, we have selected a bunch of 38 largecap tech stocks listed on the NYSE.
Output:
Output:
Cumulative Returns: 1.0314663731001577 Sharpe Ratio: 0.0038672646408557058 Max Drawdown: 0.03183340726727493
Output:
From the above plots, it can be seen that the strategy yielded a modest positive return with a relatively low riskadjusted performance, as indicated by the Sharpe Ratio. Additionally, the maximum drawdown was moderate, suggesting some degree of volatility in the strategy's performance.
It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.
Now, let us see the importance and role of the ranking scheme in long short equity strategy.
The choice of ranking scheme is the most critical component of this strategy. In our example, we used a 1day return to rank our stocks. Such a technical factor can be coupled with other indicators like moving averages, volume measures, etc.
It is also a very important decision whether to use momentum or mean reversion when ranking the stocks as different stocks would have different behaviours.
Another popular strategy is to use fundamental factors like the value and performance of the firms using a combination of P/E ratio, P/B ratio, profit margins, earnings growth, and other fundamental factors to come up with a ranking scheme.
For example, the QMJ(Quality Minus Junk) portfolio of the AQR capital management company, ranks its stocks based on a quality score. This quality score is formed by combining three fundamental factors: profitability, growth and safety.
We will discuss the relevance of choosing the capital allocation for the long short equity strategy next.
Once the ranking process is completed, the allocation of capital across stocks becomes crucial for the strategy's performance. In our approach, we utilised the equalweighted method, allocating the same weight to all stocks.
Alternatively, weights could be assigned based on daily returns, giving higher weights to stocks deviating more from average returns. Another common method is market capitalisation based weighting, which reduces exposure to volatile smallcap firms.
Rebalancing the frequency plays an important role in the long short equity strategy and we will see that next.
It is important to determine the period over which a particular strategy will give results. For example, since we were using price data, we were able to predict only for the next day accurately. Nevertheless, we can definitely predict multiple days’ returns based on price data, but the accuracy will not be as high as compared to choosing fundamental factors for predicting weekly or monthly returns.
The rebalancing frequency has an impact on transaction costs but at the same time it is slow in reacting to adverse movements in some portfolio stocks.
Next we will see the risk management and industry trends in long short equity strategy.
As with all strategies, this strategy also comes with risk. The risk lies in the deviation of the performance of the stocks selected in the portfolio from the expectation.
In the above example, if the securities on the long side see a fall in price and the securities on the short side see price rise, then the portfolio will suffer losses. Prudent risk management is required such as squaring of the stocks on hitting stop loss and keeping profit cap at the individual stock level.
Apart from this, the portfolio must be reconstructed with fresh stocks at regular intervals and the portfolio must hold a large number of stocks. This will help to limit concentration on a stock. A typical sector exposure and the top 5 long short holding of AQR longshort fund is shown below. As you can see the fund is highly diversified with limited exposure to any particular sector.
Similarly, instead of taking large concentrated holding in a particular stock, it holds small quantities of different stocks in order to avoid exposure to company specific risks. Also it can be seen that overall the portfolio is somewhat marketneutral with a slight bias towards the long side. This is in fact a latest industry trend, where more and more hedge funds are biased towards the long side to capitalise on rising equity markets.
Another important concept in long short equity strategy is that of transaction costs and slippages which we will see next.
Like any algorithmic trading strategy, for practical application, one must take into account the transaction costs that might come associated with it. Often strategies that might seem profitable might not be once you take into account the transaction costs and slippages.
Since in our strategy, we are taking new trades daily, there would be a large number of trades and hence a significant amount of transaction costs. On the other hand, trades taken based on fundamental factors would be over a month or a quarter and hence, there will be a lesser number of trades and lower transaction costs.
Slippage denotes the variance between the anticipated and actual execution prices of a trade. It can arise from several factors like market volatility, limited liquidity, or substantial trade volumes. The impact of slippage on a trading strategy's overall profitability can be significant, especially in scenarios involving frequent trading or large transactions.
For instance, if a strategy is initially tested assuming a slippage and transaction cost of 0.1% per trade, but subsequent cost analysis reveals higher costs, adjustments may be necessary. Modifying the assumed transaction and slippage costs to 0.2% during strategy testing and development ensures more realistic and accurate backtest results. This adjustment enables traders to account for actual market conditions, thereby enhancing the reliability of their strategies. ⁽³⁾
The transaction costs cost depends on the particular broker's commissions. Each broker charges a different transaction cost. For example, AmeriTrade charges a commission and a spreadbased cost in Forex, while Interactive Brokers don't charge spreadbased, they only charge a commission.
If there are two brokers who charge only commissionbased cost or spread based cost, they will have different values for that commission or the spread. These costs should be evaluated by the trader carefully before proceeding. Hence, it's the trader's responsibility to find out the transaction cost values that the broker charges.
Let us find out the applications of long short equity strategy now.
The longshort equity strategy finds broad application across various investment contexts. It is commonly employed by hedge funds, institutional investors, and individual traders seeking to capitalise on both bullish and bearish market conditions. This strategy is utilised for portfolio diversification, risk management, and enhancing riskadjusted returns. Moreover, longshort equity strategies are applied in sectors ranging from equities and derivatives to alternative investments, including commodities and currencies.
Additionally, this approach can be tailored to specific investment mandates, such as targeting alpha generation, managing volatility, or implementing marketneutral strategies. Overall, the versatility and adaptability of the longshort equity strategy make it a valuable tool in the investment toolkit across different market environments and investor objectives.
There are some advantages which we will briefly discuss next concerning the long short equity strategy.
Below are some of the most useful pros of long short equity strategy.
Let us see some cons to be wary of while using the long short equity strategy.
These are some of the cons of long short equity strategy. You can see the same below.
The longshort equity strategy, popular among hedge funds, offers a balanced approach to capitalising on market movements. By simultaneously taking long and short positions in equities, investors aim to enhance riskadjusted returns while minimising overall market exposure. This strategy, rooted in historical trends and financial theory, has evolved with advancements in technology and regulatory changes. Its returns stem from stock selection, market timing, and factor exposures.
Various types of longshort equity funds cater to diverse market conditions and investor preferences, from sectorspecific to marketneutral approaches. Despite misconceptions, successful implementation doesn't necessarily rely on complex mathematical models and is not exclusive to hedge funds. Building a longshort equity strategy involves defining the universe, ranking securities, allocating capital, and managing risk. Key considerations include the ranking scheme, capital allocation, rebalancing frequency, risk management, and transaction costs.
If you wish to learn more about long short equity strategies and the like, you must explore our Learning Track titled Advanced Algorithmic Trading Strategies which consists of various courses for traders who wish to improve their trading outcomes by using statistical analysis. Learn new strategies such as momentum, meanreversion, index arbitrage, longshort, and triplets, generate time series, and crosssectional alphas, the ways to combine and optimise alphas, as well as the ins and outs of mediumfrequency trading (MFT) and order flow analysis. Besides, you will get handson training in Python and live trading deployable models. Enroll now!
Author: Chainika Thakar (Originally written by Ishan Shah and Aaryaman Gupta)
Note: The original post has been revamped on 17^{th} April 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>But there is a risk to the strategy, that is, if the stock goes up then your stock would get sold off at expiry. So, instead of waiting for the option to expire, you can buy it back for a lesser premium.
There are many ways to use machine learning for trading and covered call strategy can be also utilised with machine learning. In this blog, we will see how you could use a simple decision tree algorithm to predict a shortterm move in the option premium price and pocket the difference (stock price and premium) while holding the stock.
This blog covers:
Machine learning in finance refers to the application of algorithms and statistical models by computers to analyse and interpret financial data, make predictions, and automate decisionmaking processes. This field leverages the vast amounts of data available in financial markets, including stock prices, trading volumes, economic indicators, and customer transaction histories, among others.
Some common applications of machine learning in finance include:
Overall, machine learning is increasingly being used in finance to automate processes, improve decisionmaking, and gain insights from large and complex datasets.
Let us now move further to find out the basics of options trading.
Options trading is a type of derivative trading where participants, known as options traders, enter contracts that provide them with the right, but not the obligation, to buy (via a call option) or sell (via a put option) a specific underlying asset at a predetermined price (known as the strike price) within a specified period of time (referred to as the expiration date).
Here are the basics of call options:
Here, a put option seller profits when the price of underlying goes above the strike price. That way the put option seller can pocket the premium. Since the buyer of the option will not be going ahead with the contract, the option will expire worthlessly.
The prices of call options and put options are influenced by several factors, including:
Understanding call options and put options and their basic mechanics is essential for investors looking to engage in options trading. Let us now gather some knowledge about covered calls.
Covered calls is a strategy used in options trading where an investor holds a long position in an underlying asset (such as stocks) and simultaneously sells call options on the same asset. The call options sold are "covered" because the investor already owns the underlying asset, which can be delivered if the option is exercised.
Here's how it works:
Position: The investor holds a certain number of shares of a particular stock.
Sell Call Options: The investor sells call options on the same stock. Each call option typically represents a number of shares which can vary. In our examples in this blog, we will be assuming them to be 100 shares of the underlying stock. By selling call options, the investor receives a premium from the buyer of the option.
Expiration: The call options have a predetermined expiration date. Until this date, the buyer of the call option has the right to purchase the underlying shares from the investor at the specified strike price.
Outcome Scenarios:
Example:
Let's say an investor owns 100 shares of XYZ Company, currently trading at $50 per share. The investor decides to sell one covered call option contract with a strike price of $55 and an expiration date one month from now. The premium received for selling this call option is $2 per share (total premium of $200).
Scenario 1: If the stock price remains below $55 at expiration, the call option expires worthless. The investor keeps the $200 premium received from selling the call option.
Scenario 2: If the stock price rises above $55 at expiration, let's say to $60 per share. The buyer of the call option exercises their right to buy the shares at $55 per share. The investor sells the shares at $55 per share, realising a profit of $5 per share ($55  $50), but forgoes potential additional gains beyond the strike price. The investor still keeps the $200 premium received from selling the call option.
Moving forward, we can now dive deeper into the topic and learn about the machine learning in covered calls.
Covered call strategy can use Machine Learning in several ways to enhance decisionmaking, optimise strategies, and improve outcomes.
Here are some applications of machine learning in covered calls:
Now that we know about covered calls and applications of machine learning in covered calls, let us move to the implementation of covered call strategy using machine learning.
Let us now see an example, using the S&P 500. S&P 500 is a U.S. index that tracks the stock performance of 500 of the largest companies listed on stock exchanges in the United States of America.
To execute the strategy, we assume that we are holding the futures contract and then we try to write a call option on the same underlying. To do this, we train a machine learning algorithm on the past data consisting of various greeks, such as IV, delta, gamma, vega, and theta of the option as the input. And the dependent variable or the prediction would be made on the next day’s return. We write the call whenever the algorithm generates a sell signal.
To begin with, let us import the necessary libraries.
First, let us import the data. I have two datasets, one with the continuous data of the Futures Contract and another with the continuous data of the 4600 strike call option. Here, by continuous we mean “across various expiries”.
The data in the csv file used in this blog is downloaded from the NASDAQ website. Let us print the data sets to visualise them.
Output:
So, we need to preprocess the data to ensure that it is ready for the Machine learning model.
Output:
['Date', 'Opt_LTP', 'Fut_LTP', 'Time_to_Expiry']
Above, we have dropped the rows with missing values and have extracted features into ‘X’ by dropping specified columns.
Then, we set the target variable y to the 'Signal' column.
Now, we will split the data into training and testing datasets. Next, we will use the first 95% of the data as the train data and the last 5% for prediction.
So, we will use the first 116 days data for training the algorithm and the last 7 days ( 1 week) of trading data to predict its performance.
Output:
((116, 5), (7, 5), (116,), (7,))
Next, we instantiate a sample decision tree and fit the train data to make predictions on the test data. We will evaluate the performance of the strategy by calculating the returns (in terms of call premium) of the strategy and then adding every day’s return for the data in the test dataset.
We will also print the accuracy and profit of the strategy.
Output:
X_train shape: (116, 5) y_train shape: (116,) Accuracy: 0.42857142857142855 Profit: 0.09999999999999999
Depending on the random state of the algorithm, the profit results might vary, but the accuracy would be close to the value above. The graph plotted above represents the cumulative returns generated by the covered call strategy over time based on the signals predicted by the decision tree classifier.
It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.
Let us see one real world example of the successful covered call strategy ahead.
While not exclusively focused on covered calls, Warren Buffett's investment philosophy often involves selling put options, which is similar to covered call strategies. ⁽¹⁾
In 2008, Buffett famously entered into a covered call strategy on his holdings in CocaCola. By selling call options against his CocaCola shares, Buffett generated additional income while still maintaining his longterm investment in the company.
Going forward, there are some risks and considerations that we will see which will help you be prepared during your journey with covered call strategy in trading using machine learning models.
Below are some risks and considerations below that a trader should be aware of.
Besides risks, there are considerable benefits that can help you with understanding the covered call strategy with machine learning.
There are several benefits also which are as follows:
Let us see the regulatory landscape around machine learning concerning finance for knowing and taking care of the legal framework.
The regulatory landscape surrounding Machine Learning in finance is as follows: ⁽²⁾
Now, we will find out answers to frequently asked questions so that you can be more clear regarding the covered call strategy using Machine Learning.
The following are some of the frequently asked questions regarding covered call strategy using machine learning:
Q: How does machine learning improve the effectiveness of covered call strategies?
A: Machine learning improves the effectiveness of covered call strategies by analysing vast amounts of historical market data and identifying complex patterns and trends that may not be apparent through traditional analysis methods. By leveraging advanced algorithms, machine learning models can:
Q: What are the key algorithms used in machine learning for covered call strategy?
A: Let us now find out the key algorithms used in machine learning for the covered call strategy:
Q: Can machine learning adapt to changing market conditions in covered call trading?
A: Yes, machine learning can adapt to changing market conditions in covered call trading. Machine learning models are trained on historical data but can continuously learn and evolve over time as new data becomes available. By monitoring realtime market data and adjusting model parameters accordingly, machine learning algorithms can adapt to shifting market dynamics, volatility levels, and other factors affecting covered call strategies. This adaptability allows machine learningenhanced covered call strategies to remain effective and competitive in dynamic market environments.
Q: How does the performance of machine learningenhanced covered call strategies compare to traditional methods?
A: The performance of machine learningenhanced covered call strategies might outperform traditional methods in several ways:
In the realm of covered call strategies, machine learning revolutionises trading by leveraging vast datasets to predict future price movements and optimise trades. Advanced algorithms enhance decisionmaking, adapt to market dynamics, and outperform traditional methods. By integrating machine learning, investors gain predictive insights, improve risk management, fostering innovation and efficiency in finance. Explore the power of machine learning in covered call strategies for maximum returns and informed decisionmaking.
If you wish to learn more about machine learning for options trading, you can explore the course on Machine Learning for Options Trading. With this course, you can unlock the power of machine learning to take your options trading to the next level and learn everything from model selection to forecasting options prices. Learn how to apply cuttingedge machine learning techniques to trade options strategies and analyse the performance. Enroll now!
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Author: Chainika Thakar (Originally written by Varun Divakar)
Note: The original post has been revamped on 15^{th} April 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
]]>At its core, a straddle options strategy involves the purchase of both a call and a put option with the same strike price and expiration date. This dualpronged approach allows traders to capitalise on significant price movements in either direction, irrespective of whether the market moves up or down.
In this blog, we will delve into the fundamentals of straddle options strategy, exploring how it works and how it can be leveraged to create effective trading strategies. Hence, the purpose of this article is to provide an introductory understanding of the straddle options strategy in trading which can be used to create your own straddle options trading strategy.
This blog covers:
The rationale behind the straddle options strategy lies in its ability to gain from volatility. Hence, this strategy is used when the trader expects significant price volatility in the underlying asset but is unsure about the direction of the price movement. By simultaneously holding a call and a put option, traders position themselves to benefit from sharp price swings, regardless of the underlying asset's eventual direction.
Here's a breakdown of the components of a straddle option:
If the price of the underlying asset moves significantly in either direction before the expiration date, one of the options will become profitable, offsetting the loss from the other option and potentially resulting in a net profit. ⁽¹⁾
This strategy works only when there is an uncertainty about the direction of the stock unlike TESLA’s case where Elon Musk already warned of a slowdown in 2024 as compared to 2023.
Let us consider an example here to learn about straddle strategy better.
We will use APPLE Inc. (ticker: AAPL) in our example. Here we are assuming that APPLE Inc. will release its quarterly earnings report soon. There is significant uncertainty about whether the report will exceed or fall short of market expectations. But, the traders are expecting sharp price swings seeing the market conditions.
A trader employing a straddle options strategy might purchase both a call option and a put option for APPLE Inc. with the same strike price and expiration date. Let's say the strike price is $100, and the expiration date is one month away.
Here's how the straddle strategy works.
Now, let's consider two scenarios:
In both scenarios, the straddle options strategy allows the trader to gain from the significant price movements regardless of the direction.
However, it's important to note that for this strategy to help you gain, the price movement needs to be substantial enough to cover the cost of purchasing both options, that is, the premium fee.
Next we will find out the types of straddle options strategy.
Straddle options strategy is of 2 types:
They are typically traded at or near the price of the underlying asset, but they can be traded otherwise as well.
Straddle Options Strategy works well in low IV regimes and the setup cost is low but the stock is expected to move a lot. In this strategy you will buy the Long Call and Long Put at the same exact price. Also, they have the same expiry on the same asset.
The strategy would ideally look something like this:
Now, let us see what is happening in the strategy image above.
Moneyness of the options to be purchased in this case.
It can be done by either of these methods:
Long straddle shown with the blue line (Vshape) is showing the entire strategy of call and put options combined.
Maximum Loss: Call Premium + Put Premium
At expiration, if the Strike Price is above or below the amount of the premium paid for both options, then the strategy would break even.
In either case of Strike Price being above or below,
It can be described as below:
But how to gain from straddle strategy?
Let us find that out now.
Continuing the above example, the instrument (in this case, the AAPL stock), if drastically moves in either direction, or there is a sudden and sharp spike in the IV, that is the time when the Straddle can be profitable. This is when either of the two scenarios discussed above as
Hence, more the probability of the volatility, more the gains. This means that there is a high possibility of substantial Profit, and the Maximum Loss would be that of the Premiums paid.
Now, if the market moves by less than 10%, then it is difficult to make a profit on this strategy. The Maximum Risk materialises if the stock price expires at the Strike Price.
We will see the implementation of straddle options next.
We will use the APPLE (Ticker – NASDAQ: AAPL) option for this example.
Traders benefit from a Long Straddle strategy if the underlying asset moves a lot, regardless of which way it moves. The same has been witnessed in the share price of AAPL.
Take a look at the chart below plotted with Python to find out the movement in share price in the last one month.
Output:
There has been a lot of movement in the stock price of AAPL, the highest being $189 and lowest being $172.5 in the last 1 month which is the current value.
Here is the option chain of AAPL for the expiry dates of April 2024. We can choose a date:
For the purpose of this example; I will buy 1 in the money Put and 1 out of the money Call Options for expiry of April 5, 2024.
I will pay $0.04 for the call with a strike price of $200 and $29.25 for the put with a strike price of $200. The options will expire on April 5, 2024 and to make a gain out of it, there should be a substantial movement in the AAPL stock before the expiry.
The net premium paid to initiate this trade will be $29.29.
To find the breakeven points for this strategy, let us see the calculation below:
Breakeven on the Upside (Call Option):
The breakeven point for the call option is the strike price plus the premium paid.
Breakeven on the Downside (Put Option):
The breakeven point for the put option is the strike price minus the premium paid.
The overall break even points for your straddle options strategy are as follows:
Therefore, for this straddle options strategy to break even or turn a profit, the stock price must move above $200.04 or below $170.75 before the expiration date of April 5, 2024. Any movement beyond these points will result in potential gains for the strategy.
Considering the amount of volatility in the market, and taking into account the market recovery process from the recent downfall we can assume that there can be an opportunity to book a profit here.
Let us now see the calculation and plotting of straddle strategy’s payoff with Python.
Now, let us see the visualisation of the Payoff chart using Python programming.
We define a function that calculates the payoff from buying a call option. The function takes sT which is a range of possible values of the stock price at expiration, the strike price of the call option and premium of the call option as input. It returns the call option payoff.
We define a function that calculates the payoff from buying a put option. The function takes sT which is a range of possible values of the stock price at expiration, the strike price of the put option and premium of the put option as input. It returns the put option payoff.
The final output would look like this:
Max Profit: Unlimited
Max Loss: 29.29
From the above plot, in the straddle options strategy result, it is observed that the max profit is unlimited and the max loss is limited to $29.9. Thus, this strategy is suitable when your outlook is moderately bearish on the stock.
As mentioned above in the calculation of break even points, we can see in the plot also that, the Break Even Point on the Upside is $200.04. Here, the call option becomes profitable, while the put option may expire worthless.
Also, the Break Even Point on the Downside is $170.75. Here, the put option becomes profitable, while the call option may expire worthless.
It is important to note that backtesting results do not guarantee future performance. The presented strategy results are intended solely for educational purposes and should not be interpreted as investment advice. A comprehensive evaluation of the strategy across multiple parameters is necessary to assess its effectiveness.
In this article we have covered all the elements of Straddle Options Strategy using the data from real life (for the example) and by understanding how the strategy can be calculated in Python. ⁽²⁾
It is the exact opposite of the Long Straddle Options Strategy. However, Long Straddle is often practised than Short Straddle.
This was about the straddle strategy, but there are some limitations also of this strategy for which there are solutions which you must know about which we will discuss in the next section.
Limitation 
Explanation 
Overcoming Strategy 
High Cost 
Straddle options involve purchasing both a call and a put option, leading to higher upfront costs. 
Spread out premium costs by using options with longer expiration dates or opting for atthemoney or slightly outofthemoney options to reduce initial investment. 
Timing the Market 
Straddle options require precise timing to capitalise on anticipated price movements. 
Diversify the portfolio with a mix of strategies and adjust the allocation of straddle options based on market conditions to mitigate the risk of mistiming the market. 
Limited Profit Potential 
Straddle options have limited profit potential if the underlying asset fails to move significantly in either direction. 
Implement a stoploss strategy to limit losses if the market doesn't move as anticipated and ensure that potential profits are protected. 
Market Volatility 
Straddle options can be less effective in lowvolatility environments, as they rely on significant price movements to generate profits. 
Monitor volatility levels and adjust your strategy accordingly. Explore alternative strategies such as iron condors or butterfly spreads that benefit from lower volatility. 
Event Risk 
Straddle options strategies are susceptible to event risk, such as unexpected market developments or announcements. 
Implement risk management measures such as stoploss orders or position sizing to mitigate potential losses from adverse events. 
Complex Strategy 
Straddle options can be complex to implement and manage, requiring a deep understanding of options pricing and market dynamics. 
Educate yourself thoroughly on options trading and practice with paper trading or small positions before committing significant capital. 
Liquidity Constraints 
Options with low liquidity may have wider bidask spreads, impacting the costeffectiveness of straddle strategies. 
Focus on liquid options contracts with tight spreads to minimise transaction costs and improve execution quality. 
By addressing these limitations with proactive strategies and risk management techniques, traders can enhance the effectiveness of straddle options strategies and improve their overall performance in the market.
In the dynamic world of finance, options trading offers a versatile toolset for navigating market volatility. Among these strategies, the straddle option stands out for its ability to profit from significant price movements, regardless of direction. Through thorough analysis and implementation techniques, traders can leverage Python to optimise straddle options strategies effectively.
However, it's essential to acknowledge and mitigate limitations such as high costs, timing challenges, and market volatility. By adopting proactive risk management and continuously refining their approach, traders can enhance the profitability and resilience of their straddle options strategies in diverse market conditions.
If you wish to learn more about straddle options strategy, then you should explore this course on Options Volatility Trading: Concepts and Strategies. With this course, you will dive into the basics to advanced topics revolving around options trading and how to gain from volatility with options strategies such as straddle options strategy. Join us on this options volatility trading journey today!
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Author: Chainika Thakar (Originally written By Viraj Bhagat)
Note: The original post has been revamped on 12^{th} April 2024 for recentness, and accuracy.
Disclaimer: All investments and trading in the stock market involve risk. Any decision to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.
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