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A new method for evaluating options based on multiquadric RBF-FD method

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  • Golbabai, Ahmad
  • Mohebianfar, Ehsan

Abstract

In this paper, a new local meshless approach based on radial basis functions (RBFs) is presented to price the options under the Black–Scholes model. The global RBF approximations derived from the conventional global collocation method usually lead to ill-conditioned matrices. Employing the idea of local approximants of the finite difference (FD) method and combining it with the radial basis function (RBF) method can result in a local meshless approach such as RBF-FD. It removes the difficulty of ill-conditionness of the original method. The new proposed approach is unconditionally stable as it is shown by Von-Neumann stability analysis. It is fast and produces high accurate results as shown in numerical experiments. Moreover, we took into account the variation of shape parameter and analyzed numerically the behavior of the RBF-FD method.

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  • Golbabai, Ahmad & Mohebianfar, Ehsan, 2017. "A new method for evaluating options based on multiquadric RBF-FD method," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 130-141.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:130-141
    DOI: 10.1016/j.amc.2017.03.019
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    References listed on IDEAS

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    1. 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.
    2. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
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    4. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
    5. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(3), pages 461-474, September.
    6. Chuang‐Chang Chang & San‐Lin Chung & Richard C. Stapleton, 2007. "Richardson extrapolation techniques for the pricing of American‐style options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(8), pages 791-817, August.
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    Cited by:

    1. Ahmad Golbabai & Omid Nikan, 2020. "A Computational Method Based on the Moving Least-Squares Approach for Pricing Double Barrier Options in a Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 119-141, January.
    2. Xubiao He & Pu Gong, 2020. "A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 999-1019, March.

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