American put options with a finite set of exercisable time epochs

The ordinary American put option assumes that investors can exercise their right at any time epoch. However, due to limitations in actual trades, they are not totally free to exercise in time. In this paper, motivated by this practical situation, we consider American put options with a finite set of exercisable time epochs. Assuming that the underlying stock price process follows a discrete-time Markov process, the put option premium is derived. It is shown that, as for the ordinary American put, the option premium is decomposed into the corresponding European put premium plus the early exercise premium under the stationary independent increments assumption. Moreover, the option premium converges to the ordinary American put premium from below as the number of exercisable time epochs increases under regularity conditions. Some lower bound of the option premium is also obtained.