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Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation

Author

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  • Mohammad Mehdizadeh Khalsaraei
  • Ali Shokri
  • Zahra Mohammadnia
  • Hamid Mohammad Sedighi
  • Efthymios G. Tsionas

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. The 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.

Suggested Citation

  • Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Zahra Mohammadnia & Hamid Mohammad Sedighi & Efthymios G. Tsionas, 2021. "Qualitatively Stable Nonstandard Finite Difference Scheme for Numerical Solution of the Nonlinear Black–Scholes Equation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, May.
    • Handle: RePEc:hin:jjmath:6679484
    DOI: 10.1155/2021/6679484
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    Cited by:

    1. Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Higinio Ramos & Zahra Mohammadnia & Pari Khakzad, 2022. "A Positivity-Preserving Improved Nonstandard Finite Difference Method to Solve the Black-Scholes Equation," Mathematics, MDPI, vol. 10(11), pages 1-16, May.

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