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Pricing European and American options by radial basis point interpolation

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  • Rad, Jamal Amani
  • Parand, Kourosh
  • Ballestra, Luca Vincenzo

Abstract

We propose the use of the meshfree radial basis point interpolation (RBPI) to solve the Black–Scholes model for European and American options. The RBPI meshfree method offers several advantages over the more conventional radial basis function approximation, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. In this paper the RBPI is combined with several numerical techniques, namely: an exponential change of variables, which allows us to approximate the option prices on their whole spatial domain, a mesh refinement algorithm, which turns out to be very suitable for dealing with the non-smooth options’ payoff, and an implicit Euler Richardson extrapolated scheme, which provides a satisfactory level of time accuracy. Finally, in order to solve the free boundary problem that arises in the case of American options three different approaches are used and compared: the projected successive overrelaxation method (PSOR), the Bermudan approximation, and the penalty approach. Numerical experiments are presented which demonstrate the computational efficiency of the RBPI and the effectiveness of the various techniques employed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:363-377
    DOI: 10.1016/j.amc.2014.11.016
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    Cited by:

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    5. Somayeh Abdi-Mazraeh & Ali Khani & Safar Irandoust-Pakchin, 2020. "Multiple Shooting Method for Solving Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 723-746, December.
    6. Shirzadi, Mohammad & Rostami, Mohammadreza & Dehghan, Mehdi & Li, Xiaolin, 2023. "American options pricing under regime-switching jump-diffusion models with meshfree finite point method," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    7. Hajimohammadi, Zeinab & Parand, Kourosh, 2021. "Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. 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.
    9. 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.
    10. Seda Gulen & Catalin Popescu & Murat Sari, 2019. "A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
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