2024 : 11 : 13
Sohrab Bazm

Sohrab Bazm

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

Title
Qualitatively Stable Schemes for the Black–Scholes Equation
Type
JournalPaper
Keywords
Black–Scholes equation; Laplace transform; nonstandard finite difference method; positivity preserving
Year
2023
Journal Fractal and Fractional
DOI
Researchers Mohammad Mehdizadeh ، Ali Shokri Shokri ، Yuanheng Wang Yuanheng Wang ، Sohrab Bazm ، Giti Navidifar ، pari khakzad

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.