High-Order Compact Scheme for Solving the Time-Fractional Black–Scholes Equation with Stability Analysis

Abstract

A high-order compact finite difference scheme on a uniform mesh is proposed for solving the timefractional Black-Scholes partial differential equation governing European-type options. The timefractional derivative is discretized using the L2 − 1σ formula, resulting in an overall accuracy of O((Δt)2 +(Δx)4). A rigorous stability and convergence analysis of the proposed scheme is presented. Numerical experiments validate the theoretical results and demonstrate the superior accuracy and computational efficiency of the proposed method compared with existing schemes.