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A family of positivity preserving schemes for numerical solution of Black–Scholes equation

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  • M. Mehdizadeh Khalsaraei

    (Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran)

  • R. Shokri Jahandizi

    (Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran)

Abstract

When one solves the Black–Scholes partial differential equation, it is of great important that numerical scheme to be free of spurious oscillations and satisfy the positivity requirement. With positivity, we mean, the component non-negativity of the initial vector, is preserved in time for the exact solution. Numerically, such property for fully implicit scheme is not always satisfied by approximated solutions and they generate spurious oscillations in the presence of discontinuous payoff. In this paper, by using the nonstandard discretization strategy, we propose a new scheme that is free of spurious oscillations and satisfies the positivity requirement.

Suggested Citation

  • M. Mehdizadeh Khalsaraei & R. Shokri Jahandizi, 2016. "A family of positivity preserving schemes for numerical solution of Black–Scholes equation," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-8, December.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:04:n:s2424786316500250
    DOI: 10.1142/S2424786316500250
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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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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