Radial basis functions with application to finance: American put option under jump diffusion

Abstract

In this paper, we consider a partial integro-differential equation (PIDE) problem with a free boundary, arising in an American option model when the stock price follows a diffusion process with jump components. We use a front-fixing transformation of the underlying asset variable to fix the free boundary conditions and approximate the integral term by the Laguerre polynomials. We use the Radial basis functions (RBF) method to achieve an implicit nonlinear system of first order equations and apply the Crank–Nicholson scheme. We apply the Predictor–Corrector method, to deal with the system of nonlinear equations. The proposed method is stable and the results are in agreement with those obtained by other numerical methods in literature.