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Pricing Options under Jump-Diffusion Models by Adaptive Radial Basic Functions

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  • Ron Chan

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 (FDM) or Finite Elements (FEM). 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 (IMQ). The method can in principle be extended to Levy-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 Chan, 2010. "Pricing Options under Jump-Diffusion Models by Adaptive Radial Basic Functions," Department of Economics Working Papers 06/10, University of Bath, Department of Economics.
    • Handle: RePEc:eid:wpaper:19329
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. 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.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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