Journal of Applied Mathematics

Journal of Applied Mathematics / 2001 / Article

Open Access

Volume 1 |Article ID 874937 | 7 pages | https://doi.org/10.1155/S1110757X01000018

On the optimal exercise boundary for an American put option

Received18 Jul 2000
Revised12 Feb 2001

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.

Copyright © 2001 Hindawi Publishing Corporation. 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.

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