Hi After searching Google I found some good reasons and I think that it might be useful for others also, So I post it here too.
The put’s payoff is bounded: at maturity, the maximal gain is K (less the premium) if the underlying is worth 0 (It is not the same with the call where the potential gain is unlimited). In the case of an American put, this fact limits the benefit of waiting to exercise: an early exercise is optimal if the underlying spot price gets low enough (interest rate). The possible risk-free arbitrage takes place when the put is deep in-the-money. An early exercise provides X. If the difference between X and the present value of X is larger than the corresponding call price, one invests PV(X), buys the call and makes the risk-free profit. (notice: the foreign risk-free rate on the foreign currency can be viewed as a dividend yield)