A weighted finite difference method for subdiffusive Black Scholes Model

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...

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Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: Krzyżanowski, Grzegorz, Magdziarz, Marcin, Płociniczak, Łukasz
Format: Article
Language:English
Subjects:
Differential equations
Finite difference method
Mathematical models
Stability analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1907.00297