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

Ron Tat Lung Chan ()
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Ron Tat Lung Chan: University of East London

Computational Economics, 2016, vol. 47, issue 4, No 6, 623-643

Abstract: 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.

Keywords: Adaptive method; Lévy processes; Option pricing; Parabolic partial integro-differential equations; Singularity; Radial basis function; The Merton jump-diffusions model (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10614-016-9563-6

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