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Title
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Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation
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Type
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JournalPaper
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Keywords
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Convergence, Nonlinear Black-Scholes equation, Nonstandard finite difference, Option pricing, Positivity-preserving, Stability.
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Abstract
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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.
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Researchers
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Hamid Mohammad Sedighi (Fourth Researcher), Zahra Mohammadnia (Third Researcher), Ali Shokri Shokri (Second Researcher), Mohammad Mehdizadeh (First Researcher)
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