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

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.