A fixed strike Asian option and comments on its numerical solution

Abstract

A boundary value formulation of an Asian option is solved with a wide range of standard textbook explicit finite difference methods including also artificial diffusion methods. We investigate the dependence of the numerical methods on the various degeneracies and approximations in the boundary value formulation. It is concluded that numerical solutions are generally oscillatory, that a simple artificial diffusion approach does not resolve this problem, but that by selecting the appropriate methods, oscillations can be avoided.