This article addresses the problem of valuing American call options with caps on dividend-paying assets. Since early exercise is allowed, the valuation problem requires the determination of optimal exercise policies. Options with two types of caps are analyzed: constant caps and caps with a constant growth rate. For constant caps, it is optimal to exercise at the first time at which the underlying asset's price equals or exceeds the minimum of the cap and the optimal exercise boundary for the corresponding uncapped option. For caps that grow at a constant rate, the optimal exercise strategy can be specified by three endogenous parameters.
Broadie, Mark, and Jerome Detemple. "American Capped Call Options on Dividend-Paying Assets." Review of Financial Studies 8, no. 1 (1995): 161-91.
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