A tempered subdiffusive Black-Scholes model

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 $2-α$ order of accuracy with respect to time, where $α\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Furthermore, we provide the stability and convergence analysis. Finally, we present some numerical results.

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