Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 643749, 8 pages
http://dx.doi.org/10.5402/2011/643749
Research Article

Fourier Transform of the Continuous Arithmetic Asian Options PDE

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, 43600 Selangor, Malaysia

Received 23 June 2011; Accepted 2 August 2011

Academic Editor: A. Bellouquid

Copyright © 2011 Zieneb Ali Elshegmani and Rokiah Rozita Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original paper is properly cited.

Abstract

Price of the arithmetic Asian options is not known in a closed-form solution, since arithmetic Asian option PDE is a degenerate partial differential equation in three dimensions. In this work we provide a new method for computing the continuous arithmetic Asian option price by means of partial differential equations. Using Fourier transform and changing some variables of the PDE we get a new direct method for solving the governing PDE without reducing the dimensionality of the PDE as most authors have done. We transform the second-order PDE with nonconstant coefficients to the first order with constant coefficients, which can be solved analytically.