  We derive the explicit price of the perpetual American put option cancelled
at the last passage time of the underlying above some fixed level. We assume
the asset process is governed by a geometric spectrally negative L\'evy
process. We show that the optimal exercise time is the first epoch when asset
price process drops below an optimal threshold. We perform numerical analysis
as well considering classical Black-Scholes models and the model where
logarithm of the asset price has additional exponential downward shocks. The
proof is based on some martingale arguments and fluctuation theory of L\'evy
processes.
