Journal of Computational Finance

Risk.net

A canonical optimal stopping problem for American options and its numerical solution

Farid AitSahlia, Tze Leung Lai

ABSTRACT

In this paper, the authors present a simple and accurate method for computing 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 and by two parameters in the presence of a dividend rate. 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 and hedge parameters.

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