Qualitatively Stable Schemes for the Black–Scholes Equation-Reference-Cited by-同舟云学术

Qualitatively Stable Schemes for the Black–Scholes Equation

Published:2023-02-04 Issue:2 Volume:7 Page:154
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Mehdizadeh Khalsaraei Mohammad¹^ORCID,Shokri Ali¹^ORCID,Wang Yuanheng²^ORCID,Bazm Sohrab¹^ORCID,Navidifar Giti¹,Khakzad Pari¹^ORCID

Affiliation:

1. Faculty of Mathematical Science, University of Maragheh, Maragheh 83111-55181, Iran

2. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

Abstract

In this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and it is shown that the new method is positive, stable, and consistent when low volatility is assumed. The efficiency of the new method is demonstrated by a numerical example.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/2/154/pdf

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