Pricing American Chooser Options

American-style options are very popular in the financial market since there is more chance to gain with the early exercise feature. With the rapid development of the American-style options, in the financial market there emerge many types of American exotic options, e.g., American strangle options, package options, compounded options and chooser options etc. among which American chooser option has not been fully understood due to the complexity of the choosing and early exercising features.The main focus of this thesis is on the pricing of American chooser options with constant volatility. American chooser options are American-style contracts written on the maximum of an American put and an American call allowing the holder to choose between a put or call option at or before a maturity date. Comparing with the European-style chooser options, the American style chooser options are more difficult to price, since there exist optimal exercise boundaries that need to be determined. In this thesis, a binomial tree method and a high-accuracy EEP collocation method are studied to evaluate the American chooser options and decide the optimal exercise boundaries.