What is the intuition behind the fact that early exercise can be optimal for an American put, but never for an American call? Assume dividend rate = 0 and interest rate > 0. The argument should make it clear why puts and calls behave differently in this respect.

I would say since we expect the price of the underlying following the risk-free rate in the future, the expected return of a put will decrease whereas the expected return of a call will stay unchanged.

Yep, if you relax your assumptions so forward can be below spot then it may be optimal to exercise a call early.

The intuition is surely that if I exercise a put early, I get money upfront which I can invest, if I exercise a call I need to borrow money. By waiting with a call I lose nothing, and might gain if the price falls below the strike. If I wait with a put, I might lose the interest earned from investing the cash. If the foregone income is greater than the possible value of waiting to see if the price rises at expiry, then early exercise is optimal.Note that this assumes that the asset pays no interim income such as a dividend - if you could get a divi by exercising a call it might be worthwhile.I'm not sure about futures - I suspect that early call exercise might be worthwhile because you could invest variation margin, but I dont know enough about futures to be sure.

If that was always the case, then the put should be exercised as soon as it is in-the-money. Clearly there is a threshold which has to be reached first. The problem is that ln S has a drift of r - sig^2/2 which can be negative if the interest rate is small enough. So it is not necessary that the expected payoff in the future is less than it is now.QuoteOriginally posted by: WillKI would say since we expect the price of the underlying following the risk-free rate in the future, the expected return of a put will decrease whereas the expected return of a call will stay unchanged.