Journal of Applied Mathematics 
Volume 2 (2002), Issue 2, Pages 71-92
doi:10.1155/S1110757X02000268

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

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.