Consider a one-step binomial model for a stock. Now, the stock is worth S₀, but will be worth either S₀u or S₀d at time T where d

(a) Consider an American put on the stock with strike price K where K > S₀u. Show that it is always better to exercise the put early when r > 0.

(b) Consider an American put with strike price K where K 0d. What is the value of the put now?

(c) Find the number such that when the strike price K is bigger than , it is better to exercise the option early and when the strike price is less than , it is better to wait until expiration.