Pricing an American Option by Approximating its Early Exercise Boundary as a Piece-Wise Exponential Function

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