Hello everyone. I'm studying (in a discrete, binomial model setting) about American options which it's owner must exercise it before expiration. 1 - Does this kind of options have some specific name?2 - Consider a 'put' on this setting i.e a derivative security that permits its owner to sell one share of stock for payment K (i.e its intrinsic value is given by K - S_n, where K is the strike price and S_n is the stock price at period n). How can I show that the optimal exercise policy is to sell the stock at time zero? (I think that his means that he should exercise his option at time zero) 3 - Considering the contract of my question 2, and given that the optimal strategy is to exercise the option at time 0, why would someone sell this kind of thing, and why would someone buy it ?Thanks in advance,Fabio

Little sense in this option unless the excercise is "triggered" by something. If TTM is 1 year and you force me to exercise in 5 months, you might call it an option with TTM of .5 years ...