Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing

Abstract

This paper develops a time-space double radial basis function (TSDRBF) method to solve PDEs arising from multiasset option pricing. By TSDRBF discretization for the high-dimensional PDEs, a linear system (LS) is obtained. After solving the LS, multi-asset options of European and American style are restored, with number N of space discretization, number M¯ of time nodes, and number M of time RBF discretization. Numerical examples confirm that the TSDRBF method has exponentially convergent rates for the number N and number M, while the convergence is linear for the number M¯. Compared with finite difference, TSDRBF avoids the difficulty of space discretization, and the convergence is greatly improved.