A tempered subdiffusive Black-Scholes model

2021/03/25 by Grzegorz Krzyżanowski, Krzyżanowski, Grzegorz, Marcin Magdziarz +1 · 1 citation
Mathematics · #65M22 #91G20 #91G60 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #G.1.8 #G.3 #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2103.13679

openalex publication_date 2021/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we focus on the tempered 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. The proposed method has the 2-α order of accuracy with respect to time, where α∈(0,1) is the subdiffusion parameter, and 2 with respect to space. Furthermore, we provide the stability and convergence analysis. Finally, we present some numerical results.

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• A New Fast Finite Difference Scheme for Tempered Time Fractional Advection-Dispersion Equation with a Weak Singularity at Initial Time

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