Qualitatively Stable Schemes for the Black–Scholes Equation

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,...

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Bibliographic Details
Published in:Fractal and fractional 2023-02, Vol.7 (2), p.154
Main Authors: Mehdizadeh Khalsaraei, Mohammad, Shokri, Ali, Wang, Yuanheng, Bazm, Sohrab, Navidifar, Giti, Khakzad, Pari
Format: Article
Language:English
Subjects:
Approximation
Black-Scholes equation
Boundary conditions
Derivatives
Finite difference method
Laplace transform
Laplace transforms
nonstandard finite difference method
Ordinary differential equations
Partial differential equations
positivity preserving
Put & call options
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Summary: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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7020154