A weighted finite difference method for subdiffusive Black Scholes Model

Grzegorz Krzy\.zanowski, Marcin Magdziarz and {\L}ukasz P{\l}ociniczak

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

Date: 2019-06, Revised 2020-04
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Citations: View citations in EconPapers (4)

Published in Computers & Mathematics with Applications 80.5 (2020): 653-670

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