Efficient Spectral-Galerkin Method for Pricing Asian Options

Abstract

This paper is concerned with a high order numerical method for evaluating the prices of Asian options with fixed strike price. We apply Legendre-Galerkin spectral method for spatial discretization and Crank-Nicholson scheme for temporal discretization. We prove that the scheme is stable for the time discretization, second order accurate in time, and exponential order convergence in space. Numerical experiments are carried out to demonstrate the efficiency and accuracy of the proposed method.