PRICING AN AMERICAN OPTION BY APPROXIMATING ITS EARLY EXERCISE BOUNDARY AS A MULTIPIECE EXPONENTIAL FUNCTION

This article proposes to price an American option by approximating its early exercise boundary as a multipiece exponential function. Closed form formulas are obtained lit terms of the bases and exponents of the multipiece exponential function. It is demonstrated that a three-poin t extrapolation scheme has the accuracy of an 800-time-step binomial t ree, but is about 130 times faster. An intuitive argument is given to indicate why this seemingly crude approximation works so well. Our met hod is very simple and easy to implement. Comparisons with other leadi ng competing methods are also included.