Journal of Applied Mathematics
Volume 1 (2001), Issue 1, Pages 39-45
doi:10.1155/S1110757X01000018
On the optimal exercise boundary for an American put option
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.
Abstract
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.