A high-order RBF-FD method for option pricing under regime-switching stochastic volatility models with jumps

Abstract

In this paper, we develop a high-order radial basis function finite difference (RBF-FD) approximation on a five-point stencil for pricing options under the regime-switching stochastic volatility models with log-normal and contemporaneous jumps (SVCJ). We fully exploit the capabilities of the RBF-FD to perform the interpolation, differentiation and integration approximations tasks required in the numerical solution of the SVCJ pricing partial integro-differential equation (PIDE). The resulting systems of equations are sparse and our treatment of the non-local integro discretisation allows an efficient implementation based on the fast Fourier transform (FFT) algorithm. We show that a local mesh refinement strategy gives high-order convergent solutions for both the European and the path dependent barrier option prices.