Consider an American put option written on a non-dividend paying stock.

Consider an American put option written on a non-dividend paying stock. The strike price is 50. The put will expire in two years. The stock price follows a two-period binomial as in the graph. At each date, the natural probability that the stock price increases is one half. The stock is currently selling at 50. A two-year annual coupon bond with annual coupon rate of 10% is selling at par. 128 80 50 48 30 18 (a) What is the price of the American put option? (b) What is the price of an American call option written on the same stock with the same strike price and expiration date? (c) Prove or disprove: the putcall parity holds for American puts and American calls