A Weighted Finite Difference Method For Subdiffusive Black-Scholes Model

In this paper we focus on the subdiffusive Black-Scholes (B-S) model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We find the governing fractional differential equation and the related weighted numerical scheme being a generalization of the classical Crank-Nicolson (C-N) scheme. The proposed method has 2 - alpha order of accuracy with respect to time where alpha is an element of (0, 1) is the subdiffusion parameter, and 2 with respect to space. Further, we provide the stability and convergence analysis. Finally, we present some numerical results. (C) 2020 Elsevier Ltd. All rights reserved.