University of Western Ontario
London, Ontario, Canada
American call options are financial derivatives that give the holder the right but not the obligation to buy an underlying security at a pre-determined price. They differ from European options in that they may be exercised at any time prior to their expiration, rather than only at expiration. Their value is described by the Black-Scholes PDE together with a constraint that arises from the possibility of early exercise. This leads to a free boundary problem for the optimal exercise boundary, which determines whether or not it is beneficial for the holder to exercise the option prior to expira Using asymptotic techniques more commonly used in other fields, such as the study of boundary layers in fluid mechanics, we find an asymptotic expressions for the location of the optimal exercise boundary near to expiration and also for the value of the option near to expiration.