Pricing by American option by approximating its early exercise boundary as a multipiece exponential function

This article proposes to price an American option by approximatingits early exercise boundary as a multipiece exponential function.Closed form formulas are obtained in terms of the bases andexponents of the multipiece exponential function. It is demonstratedthat a three-point extrapolation scheme has the accuracy ofan 800-time-step binomial tree, but is about 130 times faster.An intuitive argument is given to indicate why this seeminglycrude approximation works so well. Our method is very simpleand easy to implement. Comparisons with other leading competingmethods are also included.