International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 401547, 6 pages
http://dx.doi.org/10.1155/2011/401547
Research Article

Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

Zieneb Ali Elshegmani,1 Rokiah Rozita Ahmad,1 Saiful Hafiza Jaaman,1 and Roza Hazli Zakaria2

1School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 Bangi, Selangor D. Ehsan, Malaysia
2Department of Economics, Faculty of Economics and Administration, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 21 December 2010; Revised 2 March 2011; Accepted 2 March 2011

Academic Editor: Frits C. R. Spieksma

Copyright © 2011 Zieneb Ali Elshegmani et al. 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 work is properly cited.

Abstract

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.