Electronic Thesis and Dissertation Repository


Master of Science


Applied Mathematics


Adam Metzler


No analytical expression has been found for the optimal exercise boundary of finite maturity American put options. This thesis evaluates the performance of approximating the optimal boundary with a class of analytically tractable sub-optimal exercise boundaries which admit known first passage time density functions. The performance is evaluated in two steps, first by computing and comparing the value of the put option under the sub-optimal exercise policy to existing numerical approximation methods such as the binomial price, then by examining the profit/loss of a trader that would result from hedging and trading strategies based on the sub-optimal exercise policy. We discovered that the valuation results from sub-optimal boundary exercise is very close to the binomial price. A closed form expression for the delta of the American put under sub-optimal exercise is derived, and the formula is remarkably close to the true numerical delta at significantly reduced computational time.