A Robust Numerical Solution to a Nonlinear Time-Fractional Generalized Distributed-Order Black-Scholes Equation

Abstract

In this study, we address the generalized distributed-order time-fractional Black-Scholes equation through an implicit method. We approximate the time and spatial derivatives using finite difference techniques. Furthermore, we employ a quasi-linearization technique to remove the nonlinear term, thereby simplifying the computational process. The numerical results from our method demonstrate both its accuracy and convergence rate, establishing it as a robust approach for solving financial models. This research highlights the potential of finite differences and quasi-linearization in tackling mathematical equations in financial engineering.