Solving an Asian option PDE via the Laplace transform

ABSTRACT: Solving the Black-Scholes PDE of the arithmetic Asian options is one of the most difficult problems in financial mathematics. A variety of ways ways have been proposed to address the problem. In this study, we use the PDE approach by presenting an efficient method for pricing a continuous arithmetic Asian option. Using the Laplace transform we reduce the three-dimension partial differential equation of the arithmetic Asian option into a two-dimension ordinary differential equation. Its final analytical solution is presented. We conclude that this method is applicable to all types of arithmetic Asian options