Numerical Methods For Arithmetic Average Asian Options

In this paper,we study the numerical methods for a special parabolic partially differen-tial equation PDE,including finite difference method FDM and finite element method FEM,and their application for the Asian option pricing.Firstly,we give the parabolic partially dif-ferential equation,where the arithmetic mean Asian option satisfies under the Black-Scholes model.Then,we use the dimensionality reduction and far-field truncation techniques to transform the original problem into a bounded one-dimensional parabolic PDE.Based on these,we present the FDM and FEM schemes for the corresponding problem.Finally,the arithmetic mean is obtained by inverse dimensional transformation image of numerical solu-tion of Asian options.Numerical experiments are presented to show the effectiveness of the algorithms.