2024 : 11 : 13

Mohammad Mehdizadeh

Academic rank: Professor
ORCID:
Education: PhD.
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HIndex:
Faculty: 1
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Research

Title
Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation
Type
JournalPaper
Keywords
Convergence, Nonlinear Black-Scholes equation, Nonstandard finite difference, Option pricing, Positivity-preserving, Stability.
Year
2021
Journal Journal of Mathematics
DOI
Researchers Mohammad Mehdizadeh ، Ali Shokri Shokri ، Zahra Mohammadnia ، Hamid Mohammad Sedighi

Abstract

In this paper, we use a numerical method for solving the nonlinear Black–Scholes partial differential equation of the European option under transaction costs, which is based on the nonstandard discretization of the spatial derivatives. )e proposed scheme, in addition to the unconditional positivity, is stable, consistent, and monotone. In order to illustrate the efficiency of the new method, numerical results have been performed by four models.