Closed-form valuation of American call options on stocks paying multiple dividends

An American call option on a stock paying a single known dividend can be valued using the Roll-Geske-Whaley formula. This paper extends the Roll-Geske-Whaley model to the n dividends case by using the generalized n-fold compound option model. In this way this paper offers a closed-form solution for American options on stocks paying n known discrete dividends. Moreover, the model also offers the critical values of the early exercise boundaries at each ex-dividend date instant, making it easy to define an early exercise strategy. Numerical examples are included to illustrate this approach.