Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation

Abstract

In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation. The operator splitting scheme is used to efficiently solve the 3D time-fractional BS equation. We use a nonuniform grid for pricing 3D options. We compute the three-asset cash-or-nothing European call option and investigate the effects of the fractional-order $\alpha$ in the time-fractional BS model. Numerical experiments demonstrate the efficiency and fastness of the proposed scheme.