We show that an American put option with delivery lags can be decomposed as a
European put option and another American-style derivative. The latter is an
option for which the investor receives the Greek Theta of the corresponding
European option as the running payoff, and decides an optimal stopping time to
terminate the contract. Based on the this decomposition, we further show that
the associated optimal exercise boundary exists, and is a strictly increasing
and smooth curve. We also analyze its asymptotic behavior for both large
maturity and small time lag using the free-boundary method.Comment: 28 pages, 5 figure