Valuation and early exercise boundaries of American options

Abstract

This paper presents a simple and accurate method to compute the values and early exercise boundaries of American options. A key idea underlying the method is the reduction of American option valuation to a single optimal stopping problem for standard Brownian motion, indexed by one parameter in the absence of dividends. Numerical results obtained by this method show that in the canonical scale the stopping boundaries are well approximated by certain piecewise linear functions that can easily be tabulated, leading to new approximations for American option values. We also demonstrate how this methodology can be extended to treat American-style path-dependent options, for which there is a second state variable representing the path-dependent characteristic.