Numerical Solution of Multi-Asset Option Pricing Problems Using an Improved RBF-DQ Method

Abstract

In this paper, a modification of the original global radial basis functions-based differential quadrature (RBF-DQ) method is set forth and analyzed. The improved RBF-DQ method is applicable to the numerical approximation of solutions of a wide range of partial differential equations (PDEs) with mixed derivative terms. However, it appears to be considerably faster than the original method. In support of this contention, the multi-dimensional Black-Scholes (BS) equation in the Geometric Brownian Motion (GBM) framework has been solved numerically by using the proposed method and compared with results obtained via the original RBF-DQ method. For accuracy achieved versus work expended, the improved method performs better.