A tempered subdiffusive Black–Scholes model

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-04-09 DOI:10.1007/s13540-024-00276-2

Grzegorz Krzyżanowski, Marcin Magdziarz

引用次数: 0

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 option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order \(2-\alpha \) with respect to time, where \(\alpha \in (0,1)\) is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.

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一个有节制的亚扩散布莱克-斯科尔斯模型

在本文中，我们将重点研究节制亚扩散布莱克-斯科尔斯（Black-Scholes）模型。我们工作的主要部分包括在所考虑的模型中采用有限差分法作为期权定价的数值方法。我们推导了支配性分数微分方程和相关的加权数值方案。所提出的方法在时间上有一个精度阶（2-\alpha \），其中 \(\alpha \in (0,1)\) 是次扩散参数，在空间上有 2 个精度阶。此外，我们还提供了稳定性和收敛性分析。最后，我们给出了一些数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.