Stock Options Pricing in Financial Markets with Machine Learning

Table of Contents

1. Abstract
2. Quantitative Analysis Method
3. Dataset Description
4. Machine Learning Algorithms Used
5. Training Results for Optimal Model Selection
6. Pricing Result Visualisation
7. Prediction Error Visualisation
8. Feature Importance of the Model
9. Future Improvements

Abstract

This financial engineering project applies machine learning to price stock options using a large dataset (74,492 rows and 21 columns) from Yahoo Finance, covering 50 companies across various sectors. Among five regression models, Random Forest demonstrated the best predictive performance with low error rates and was selected for the final prediction. The model effectively identified key parameters influencing option pricing, such as bid price, stock price, and moneyness. It achieved strong evaluation metrics on the test set, with predictions closely aligning to actual pricing values.

Quantitative Analysis Method

The analysis was performed using Python in Google Colab. The methodology involved several key steps:

1. Data Collection:

   • Datasets were sourced from Yahoo Finance for 50 companies across various sectors.

2. Exploratory Data Analysis (EDA):

   • Statistical methods like summary statistics and histograms were used to explore the data.

3. Data Inspection and Cleaning:

   • Missing and empty rows were removed to ensure data integrity.

4. Feature Engineering:

   • Additional features (time_to_maturity, moneyness, and bid_ask_spread) were derived to enhance model context.

5. Feature Selection:

   • Relevant features were selected based on correlation and Variance Inflation Factor (VIF) analysis.

6. Machine Learning Model Training:

   • Five regression models (Linear Regression, Ridge Regression, Random Forest, Gradient Boosting, and Support Vector Regression) were trained, with hyperparameter tuning using RandomizedSearchCV. The best-performing model was selected for further analysis.

7. Model Evaluation and Pricing Visualisation:

   • The final model was evaluated using regression metrics (MSE, RMSE, MAE, MAPE, R-squared, and Explained Variance) with visualizations such as scatter plots and histograms created to analyse prediction accuracy.

Dataset Description

This project utilises the latest stock options datasets from 50 companies across various sectors sourced from Yahoo Finance, with datasets that refresh upon each fetch. The companies include major names such as Apple, Microsoft, Tesla, NVIDIA, and more. The raw dataset comprises 79,853 rows and 18 columns, where each row represents an options contract and columns detail parameters like strike price, implied volatility, expiration date, and more. After cleaning, 74,492 rows remain, with missing values removed. Additionally, three derived parameters: time to maturity, moneyness, and bid-ask spread were added to enhance the dataset’s analytical depth.

Column Name	Data Type	Description	Count	Mean	Min	Max	Std Dev
contractSymbol	object	Unique identifier for each contract	74,492	N/A	N/A	N/A	N/A
lastTradeDate	datetime64[ns, UTC]	Last trading date	74,492	2024-10-31	2016-03-11	2024-11-27	N/A
strike	float64	Strike price	74,492	470.57	0.50	7,500.00	719.82
lastPrice	float64	Last traded price	74,492	74.02	0.01	3,646.27	164.58
bid	float64	Current bid price	74,492	33.91	0.00	3,208.00	144.38
ask	float64	Current ask price	74,492	34.89	0.00	3,232.00	146.93
change	float64	Price change	74,492	-0.23	-367.47	774.66	7.82
percentChange	float64	Percent price change	74,492	-1.41	-99.93	7,400.00	62.01
volume	float64	Trading volume	74,492	145.81	0.00	228,429.00	2,062.93
openInterest	float64	Open contracts	74,492	30.11	0.00	41,975.00	388.52
impliedVolatility	float64	Implied volatility of options	74,492	N/A	N/A	N/A	N/A
inTheMoney	object	Indicates if option is in the money	74,492	N/A	N/A	N/A	N/A
contractSize	object	Size of the option contract	74,492	N/A	N/A	N/A	N/A
currency	object	Currency of the option	74,492	N/A	N/A	N/A	N/A
option_type	object	Type (call/put)	74,492	N/A	N/A	N/A	N/A
expiration_date	datetime64[ns]	Option expiration date	74,492	2025-06-30	2024-11-29	2027-01-15	N/A
stock	object	Stock ticker	74,492	N/A	N/A	N/A	N/A
stock_price	float64	Current stock price	74,492	459.39	17.18	5,223.15	851.55
time_to_maturity	float64	Time to expiration in years	74,492	0.58	-0.0027	2.13	0.63
moneyness	float64	Measure of intrinsic value	74,492	-0.52	-22.19	0.99	2.39
bid_ask_spread	float64	Difference between bid and ask	74,492	0.98	-94.00	40.00	3.21

Table 1: Summary of Dataset Columns and Key Statistics

Machine Learning Algorithms Used

• Linear Regression: Simple, efficient model for linear relationships.
• Ridge Regression: Regularized model to prevent overfitting.
• Random Forests: Ensemble model for large, non-linear data.
• Gradient Boosting: Reduces bias and variance via weak learner combinations.
• Support Vector Regressio: Excels in high-dimensional spaces.

Training Results for Optimal Model Selection

Model	Mean Squared Error (MSE)	Root Mean Squared Error (RMSE)	Mean Absolute Error (MAE)	Mean Absolute Percentage Error (MAPE)	R-squared (R²)	Explained Variance Score
Linear Regression	10525.431807	102.593527	48.816828	10853.778479	0.607325	0.607326
Ridge Regression	10525.430080	102.593519	48.816829	10854.118772	0.607325	0.607326
Random Forest	676.218183	26.004195	7.587412	48.047761	0.974772	0.974775
Gradient Boosting	3508.271399	59.230663	19.959248	2619.825724	0.869116	0.869122
Support Vector Regression (SVR)	15093.463847	122.855459	45.219775	5738.897342	0.436904	0.472096

Table 2: Model Evaluation Metrics for Different Regression Models

Random Forest significantly outperforms the other models, which demonstrates the best overall predictive accuracy with low error metrics (MSE: 676.22, RMSE: 26.00, MAE: 7.59) and a high R-squared value (0.97), indicating it captures the majority of the variance in the data. Gradient Boosting performs well (R-squared: 0.87), but still falls behind Random Forest in terms of prediction accuracy. Linear and Ridge Regression exhibit similar performance, with higher errors (MSE: 10525) and lower R-squared (0.61), indicating limited model fit. Support Vector Regression (SVR) performs the worst, with the highest MSE, RMSE, and MAPE, and the lowest R-squared (0.44), suggesting it is not suitable for this dataset.

Hence, Random Forest was selected for hyperparameter tuning and option pricing since it can better provide valuable insights into market behavior by identifying key parameters that influence price movements, such as implied volatility, strike price, and time to maturity.

Pricing Result Visualisation

Figure 1: Scatter plot of actual vs. predicted option prices for the Random Forest model

The red dashed line in the scatter plot represents the ideal fit, and the data points are closely aligned with the diagonal, indicating strong predictive performance and minimal prediction error. This alignment demonstrates the model's ability to accurately capture the underlying relationships in the data and generalize effectively for option pricing.

Prediction Error Visualisation

Figure 2: Histogram of prediction errors (Actual - Predicted) for the Random Forest model

The prediction error histogram displayed a distribution closely resembling a normal curve with values clustered around zero and a relatively small spread. This indicates that the model's predictions are consistently accurate with minimal fluctuation in the error values.

Feature Importance of the Model

Figure 3: Feature importance of the Random Forest model

The analysis shows that the bid price is the most important factor with a score close to 0.6, followed by stock price at 0.17 and moneyness at 0.15. Implied volatility scores lower at 0.07, while time to maturity and bid-ask spread have minimal impact. This highlights the model’s focus on key variables like bid price, stock price, and moneyness.

The bid price reflects market demand and significantly influences the option's value. Stock price determines the option's intrinsic value. Moneyness indicates whether the option is in, at, or out of the money. These three parameters directly influence an option's value as they focus on immediate and market-driven factors by reflecting market demand, the asset's current price, and the option’s intrinsic value. Although implied volatility affects the option’s premium, its influence is smaller compared to the other factors. Time to maturity and bid-ask spread have minimal impact because they are less correlated with immediate option value, which is driven by market-sensitive factors like bid price, stock price, and moneyness.

Future Improvements

Future work could focus on integrating real-time data for live pricing and using more advanced models to enhance accuracy and scalability. Leveraging GPUs would speed up training and enable the switch from randomised search to grid search for better optimisation. Migrating the Jupyter notebook to a more scalable environment would improve efficiency and simplify deployment.