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Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models

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  • Ron Tat Lung Chan

    (University of East London)

Abstract

The aim of this paper is to show that option prices in jump-diffusion models can be computed using meshless methods based on radial basis function (RBF) interpolation instead of traditional mesh-based methods like finite differences or finite elements. The RBF technique is demonstrated by solving the partial integro-differential equation for American and European options on non-dividend-paying stocks in the Merton jump-diffusion model, using the inverse multiquadric radial basis function. The method can in principle be extended to Lévy-models. Moreover, an adaptive method is proposed to tackle the accuracy problem caused by a singularity in the initial condition so that the accuracy in option pricing in particular for small time to maturity can be improved.

Suggested Citation

  • Ron Tat Lung Chan, 2016. "Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 47(4), pages 623-643, April.
    • Handle: RePEc:kap:compec:v:47:y:2016:i:4:d:10.1007_s10614-016-9563-6
    DOI: 10.1007/s10614-016-9563-6
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    References listed on IDEAS

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    1. Raymond Brummelhuis & Ron T. L. Chan, 2014. "A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(3), pages 238-269, July.
    2. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    3. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    6. Ron Chan & Simon Hubbert, 2014. "Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme," Review of Derivatives Research, Springer, vol. 17(2), pages 161-189, July.
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    Cited by:

    1. Yusho Kagraoka, 2020. "The Fractional Step Method versus the Radial Basis Functions for Option Pricing with Correlated Stochastic Processes," IJFS, MDPI, vol. 8(4), pages 1-13, December.

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