Nj. Ju, PRICING AN AMERICAN OPTION BY APPROXIMATING ITS EARLY EXERCISE BOUNDARY AS A MULTIPIECE EXPONENTIAL FUNCTION, The Review of financial studies, 11(3), 1998, pp. 627-646
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.