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 option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order \(2-\alpha \) with respect to time, where \(\alpha \in (0,1)\) is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.