A tempered subdiffusive Black-Scholes model

Abstract

In this paper, we focus on the tempered subdiffusive Black-Scholes 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 derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has the $2-\alpha$ order of accuracy with respect to time, where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Furthermore, we provide the stability and convergence analysis. Finally, we present some numerical results.