  In this paper, we study a version of the perpetual American call/put option
where exercise opportunities arrive only periodically. Focusing on the
exponential L\'evy models with i.i.d. exponentially-distributed exercise
intervals, we show the optimality of a barrier strategy that exercises at the
first exercise opportunity at which the asset price is above/below a given
barrier. Explicit solutions are obtained for the cases the underlying L\'evy
process has only one-sided jumps.
