We will derive a two-state put option value in this problem. Current stock price So = 100. Strike price X = 112. r is the interest rate which satisfies 1 +r= 1.10. The two possibilities for the future stock price St are 140 and 70. a. Show that the range of the stock price S is 70, whereas that of P, the payoff of put option, is 42 across the two states. What is the hedge ratio of the put? (4 points) b. Form a portfolio of 3 shares of stock and 5 puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio? (4 points) c. Given the stock currently is selling at 100, solve for the value of the put. (5 points)