A weighted finite difference method for subdiffusive Black Scholes Model

06/29/2019

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by   Grzegorz Krzyżanowski, et al.

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In this paper we focus on the 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 being a generalization of the classical Crank-Nicolson 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.