Data‐Driven and Numerical Approaches With PDEs for Option Pricing

This study examines the performance of various numerical and machine learning (ML) approaches in option pricing. The Black–Scholes equation is solved via finite difference (FD) methods and Laplace transform (LT), and its numerical inversions then used to price European options where the volatility of the underlying asset is calculated through the statistical measure of stock markets’ historical data. In data driven approaches, calibrated via ML, some conventional and deep learning‐based approaches are reviewed by utilising 50ETF European stock index options data. The efficiency and accuracy of the adapted methods is demonstrated by computing the conventional metrics for benchmark options. The results reveal that the numerical inversion techniques of LT with a direct solver such as Thomas algorithm are more efficient in pricing European options as compared to the classical time marching methods. When the dataset is sufficiently large the omission of some input parameters in a pricing model can still generate relatively accurate results using ML techniques.