Problem 6. An equity securities market model follows a multi-period binomial model. At each node of the binomial tree the current stock price S will branch to us in the upstate and dS in the downstate. You are given that the initial stock price is 10, u = 1.35, d=0.85 and the interest-rate is 5% effective per period. The stock does not pay dividends. (i) (3 points) Compute the price of a European put option on the stock which expires in 4 periods and has a strike price of 9.2. (ii) (4 points) Compute the price of an American put option on the stock which expires in 4 periods and has a strike price of 9.2 and describe the optimal exercise policy for this American put option. (iii) (3 points) Compute the replicating portfolio for the American put option at thime 2 if the stock moves down twice.