An efficient weak Galerkin finite element method for generalized Black-Scholes PDEs modelling option pricing

In this work, we give a thorough analysis of a weak Galerkin finite element technique (WG-FEM) designed specifically for the generalized Black-Scholes equation-based numerical calculation of option price valuation. This novel method offers a strong and adaptable framework for handling the complexity of option pricing models by combining the weak Galerkin method for spatial discretization with the backward-Euler scheme for time discretization. In this study, we aim to establish stability and optimal order error estimates and we obtain these error estimates by a rigorous theoretical study, proving the stability and convergence characteristics of the proposed WG finite element scheme. We perform extensive numerical experiments to validate our theoretical results. These examples are carefully chosen to demonstrate the WG-FEM practical efficacy and dependability in various scenarios and parameter settings.