An Improved Method for Pricing and Hedging American Options

The majority of quasi-analytic pricing methods for American options are efficient near-maturity but are prone to larger errors when time-to-maturity increases. A new methodology, called the "extension"-method, is introduced to increase the accuracy of almost any existing quasi-analytic approach in pricing long-maturity American options. It relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches so that the maturity range for which small errors are attainable is extended. The new methodology retains the quasi-analytic nature of the methods it improves on and we derive generic quasi-analytic formulae for the price of an American put as well as for its delta parameter. Our numerical study indicates that the proposed methodology considerably improves both the pricing and the hedging performance of a number of established approaches for a wide range of maturities. Furthermore, the pricing improvements are most sizeable at longer maturities, where existing approaches do not perform well.