On five-point equidistant stencils based on Gaussian function with application in numerical multi-dimensional option pricing

Abstract

The purpose of this article is to study how the integrals of the Gaussian radial basis function can be employed to produce the coefficients of approximations under the radial basis function - finite difference solver. Here these coefficients are reported for a five-point stencil. Error equations are derived to demonstrate that the convergence rate is four for approximating the 1st and 2nd differentiations of a function. Then the coefficients are used in solving multi-dimensional option pricing problems, which are modeled as time-dependent variable-coefficients parabolic partial differential equations with non-smooth initial conditions. The numerical simulations support the applicability and usefulness of the presented method.