Journal of Applied Mathematics
Volume 1 (2001), Issue 1, Pages 39-45

On the optimal exercise boundary for an American put option

Ghada Alobaidi and Roland Mallier

Department of Applied Mathematics, The University of Western Ontario, London N6A 5B7, ON, Canada

Received 18 July 2000; Revised 12 February 2001

Copyright © 2001 Ghada Alobaidi and Roland Mallier. 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.


An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying PDE, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit.