Problem 3: Multi-Period Binomial Model. A non-dividend paying stock with current share price of $20 can either go up or down by 20% in each of the next two months, with up occurring 55% of the time and down occurring 45% of the time. The risk-free rate is 10% per year. Consider an American put with a strike price of $22 expiring in two months. (a) Construct the 2-period binomrial tree to represent the evolution of the stock price. (b) What are the option's payoffs if it is held to the maturity date? (c) What is the value of the American put one month from now if the stock price becomes $24? 4 (d) What is the value of the American put one month from now if the stock price becomes $16 ? (e) What is the value of the American put today