Journal of Applied Mathematics
Volume 2 (2002), Issue 2, Pages 71-92

Evaluating approximations to the optimal exercise boundary for American options

Roland Mallier

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

Received 24 March 2001; Revised 5 October 2001

Copyright © 2002 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.


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.