Pricing options with XGBoost

Options are financial derivatives used for risk management and speculation, for example, and have been studied extensively in order to forecast its price. Before the technological revolution, parametric models were used with strict assumptions to forecast the options price, such as the Black-Scholes Model. Since then, Machine Learning models, such as the XGBoost model have been created to make forecasts without such strict assumptions from parametric models. The purpose of this dissertation is to show how the XGBoost model can forecast option prices accurately using variables from the BSM. In addition, by using the struc- ture of the standard deviation, third and fourth moment of the distribution of the stock price, the days to the next dividend and the next dividend to be paid, this study aims to understand by how much it improves the price forecasted from the XGBoost model with variables from the BSM. Thus, options from 100 of the biggest companies in the S&P 500 between November and February of 2020 are used to train and test the two XGBoost models. The BSM is used as the benchmark. The results are very favorable towards the XGBoost models since the RMSE of the first and the second model are lower than the BSM by 29.51% and 35.47% , respec- tively. When looking at the options by its distance to the strike price, the XGBoost models always perform better than the BSM, but when the latter has a terrible per- formance for ITM, XGBoost has a bad performance too. For OTM put options, BSM underprices the options while XGBoost models don’t. For short maturities, the XGBoost models don’t improve the performance relative to the BSM by much. Although, they provide a good forecast when compared to BSM for options with long maturities. In a nutshell, the second XGBoost model is always better than the first and almost always they forecast with better accuracy and less bias than the BSM.