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. Thestock is currently selling at 50 . A two-year annual coupon bond with annual coupon rate of 10% is selling at par. (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 strikeprice and expiration date? (c) Show that the put-call parity does not hold for American puts and calls here. Explain whythis could happen. (d) If you are allowed to change one number of this example, the put-call parity could hold. Which number would you change and to how much? Explain