An analytic solution to the American put problem is derived herein. The hedge ratio
and other derivatives of the solution are presented. The formula derived implies
an exact duplicating portfolio for the American put consisting of discount bonds
and stock sold short. The formula is extended to consider put options on stocks paying
cash dividends. A polynomial expression is developed for evaluating these formulae.
Values and hedge ratios for puts on both dividend and nondividend paying stocks are
calculated, tabulated, and compared with values derived by numerical integration
and binomial approximation. As with European options, evaluating an analytic formula
is more efficient than approximating the stock price process or the partial differential
equation by binomial or finite difference methods. Finally, applications of this
American put solution are discussed.