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arXiv · 1907.00297

A weighted finite difference method for subdiffusive Black Scholes Model

Grzegorz Krzyżanowski·Marcin Magdziarz·Łukasz Płociniczak
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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.

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Grzegorz Krzyżanowski, Marcin Magdziarz, Łukasz Płociniczak. 2019-06-29. A weighted finite difference method for subdiffusive Black Scholes Model. https://doi.org/10.1016/j.camwa.2020.04.029

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