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A New Stable Local Radial Basis Function Approach for Option Pricing

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  • A. Golbabai

    (Iran University of Science & Technology)

  • E. Mohebianfar

    (Iran University of Science & Technology)

Abstract

In this paper, we develop a new local meshless approach based on radial basis functions (RBFs) to solve the Black–Scholes equation. The global RBF approximations derived from conventional global collocation method usually lead to ill-conditioned matrices. The new scheme employs the idea of the finite difference method to localize them. It removes the difficulty of ill-conditioning of the original method. The new proposed approach is unconditionally stable as it is shown by Von-Neumann stability analysis. As well as it is fast and it produces accurate results as shown in numerical experiments.

Suggested Citation

  • A. Golbabai & E. Mohebianfar, 2017. "A New Stable Local Radial Basis Function Approach for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 271-288, February.
    • Handle: RePEc:kap:compec:v:49:y:2017:i:2:d:10.1007_s10614-016-9561-8
    DOI: 10.1007/s10614-016-9561-8
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    References listed on IDEAS

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    1. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893.
    2. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.
    3. 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.
    4. 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.
    5. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    6. 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.
    7. 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.
    8. 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. Slobodan Milovanovi'c & Victor Shcherbakov, 2017. "Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methods," Papers 1711.09852, arXiv.org, revised Aug 2018.
    2. Haq, Sirajul & Hussain, Manzoor, 2018. "Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 248-263.
    3. 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.

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