Journal of Applied Mathematics

Journal of Applied Mathematics / 2002 / Article

Open Access

Volume 2 |Article ID 807303 | https://doi.org/10.1155/S1110757X02000268

Roland Mallier, "Evaluating approximations to the optimal exercise boundary for American options", Journal of Applied Mathematics, vol. 2, Article ID 807303, 22 pages, 2002. https://doi.org/10.1155/S1110757X02000268

Evaluating approximations to the optimal exercise boundary for American options

Received24 Mar 2001
Revised05 Oct 2001

Abstract

We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry. By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, and compare this value to the actual value of the option. This gives an alternative method to evaluate approximations. We find the series solution for the call performs excellently under this criterion, even for large times, while the asymptotic approximation for the put is very good near to expiry but not so good further from expiry.

Copyright © 2002 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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