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 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.
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