Approximating American options and other financial contracts using barrier derivatives

Despite more than twenty-five years of efforts, valuation of the American put and similar free-boundary problems remains a perplexing enigma. These problems have escaped true analytical solutions and still must be solved by numerical methods. Over the years, a number of approximations have been proposed. This paper describes another approximation method based on barrier options. The exercise policy is approximated by a simple class of functions, and the best policy within that class is selected by standard optimization techniques. The resulting value is generally a very tight lower bound to the true option value. The advantages of this method are its simplicity and speed, even when used in general-purpose computer programs such as spreadsheets.