We will derive a two-state put option value in this problem. Data: S0 = 190; X = 200; 1 + r = 1.1. The two possibilities for ST are 220 and 120. a. The range of S is 100 while that of P is 80 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Hedge ratio ______

b-1. Form a portfolio of 4 shares of stock and 5 puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.)

Nonrandom payoff $ ______

b-2. What is the present value of the portfolio? (Round your answer to 2 decimal places.)

Present value $ _______

c. Given that the stock currently is selling at 190, calculate the put value. (Round your answer to 2 decimal places.)

Put value $ ________