We will derive a two-state put option value in this problem. Data: S_0 = 100; X = 110; 1 + r = 1.10. The two possibilities for S_T are 130 and 80. a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put? b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio? c. Given that the stock currently is selling at 100, solve for the value of the put. d. Calculate the value of a call option on the stock in the previous problem with an exercise price of 110. Verify that the put-call parity theorem is satisfied by your answers to problems c and d