Journal of Applied Mathematics
Volume 2013 (2013), Article ID 128025, 7 pages
http://dx.doi.org/10.1155/2013/128025
Research Article

A Simple Numerical Method for Pricing an American Put Option

Beom Jin Kim,1 Yong-Ki Ma,2 and Hi Jun Choe1

1Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea
2Department of Applied Mathematics, Kongju National University, Chungcheongnam-Do, Gongju 314-701, Republic of Korea

Received 24 October 2012; Revised 4 January 2013; Accepted 15 January 2013

Academic Editor: Shan Zhao

Copyright © 2013 Beom Jin Kim 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

We present a simple numerical method to find the optimal exercise boundary in an American put option. We formulate an intermediate function with the fixed free boundary that has Lipschitz character near optimal exercise boundary. Employing it, we can easily determine the optimal exercise boundary by solving a quadratic equation in time-recursive way. We also present several numerical results which illustrate a comparison to other methods.