A closed-form formula for unprotected American call options on assets paying discrete known dividends

In general, American options cannot be valued by closed-form formulas. There is however an exception within the setting of dividendpaying assets. It is known that American call options will be exercised early, only at a time just prior to an ex-dividend date. In extending the Roll-Geske-Whaley model and in using the theory of the n-fold compound options, such closed-form formulas are derived in case the asset pays n dividends with n > 2. Moreover a sensitivity analysis for American call options will be performed. Finally some numerical examples are included.