We will derive a two-state put option value in this problem. Data: S= 100; x=- 110; 1 + r= 1.10. The two possbilities for Sr are 130 and 80.

a. Show the range of S is 50 while 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 ratio to this portfolio?

c. What is the present value of the portfolio?

d. Given that the stock currently is selling at 100, show that the value of the put must be 10.91.