A weighted finite difference method for subdiffusive Black Scholes Model

Abstract 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 − α order of accuracy with respect to time where α ∈ ( 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.