Machine Learning Methods for Predicting European Options on Bitcoin and S&P 500 with Lag Intervals and Volatility Estimation

Options are widely recognized as essential financial instruments among investors and practitioners due to their ability to hedge against risks, particularly in assets with varying levels of volatility. High-volatility assets, such as cryptocurrencies like Bitcoin, and less volatile assets, like stocks such as the S&P 500, both benefit from the risk management capabilities of options. This research aims to predict the prices of call and put options for Bitcoin and the S&P 500 using two powerful machine learning models, eXtreme Gradient Boosting (XGBoost) and Light Gradient Boosting Model (LightGBM). Both models were fine-tuned using hyperparameter optimization techniques, including DataRobot and GridSearchCV, to achieve the best performance. To enhance the analysis, the study divided the prediction models into three groups: based on lag intervals (1, 7, 15, and 30), based on volatility estimation methods (realized variance, bipower variation, and signed jumps variation), and a combination of volatility estimation methods and lag intervals. The results indicate that for Bitcoin options, shorter lags generally yield more accurate predictions compared to longer lags such as lag 30. On the other hand, for the S&P 500, lag 30 remains relevant and provides optimal predictions, likely reflecting the more stable nature of stock market dynamics. Among the volatility estimation methods, bipower variation was found to deliver the most accurate predictions for both Bitcoin and S&P 500 options. Overall, the study also highlights that XGBoost consistently outperforms LightGBM across almost all datasets. Furthermore, the results reveal that predicting Bitcoin option prices yields better accuracy compared to predicting S&P 500 option prices, which could be attributed to the distinct characteristics of the assets and the higher sensitivity of Bitcoin to recent market changes. These findings emphasize the significance of model selection and feature engineering in improving option price predictions.