On the construction of a quartically convergent method for high-dimensional Black-Scholes time-dependent PDE

Abstract

There exist several numerical methods for finding the resolution of high dimensional option pricing Black-Scholes PDE with variable coefficients. Here we use radial basis functions to produce differentiation stencils (abbreviated by RBF-FD) on uniform point sets. In fact, the target is to propose a fully quartically convergent scheme via the RBF-FD methodology along both time and space directions. We too present a stability analysis for the selection of the time step size when the spatial step sizes vary. Furthermore, we draw a conclusion by several challenging computational experiments in high dimensions and reveal the superiority and the robustness of the scheme.