Chapter 16, Problem 8PS

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 $S_1$ are $\text{13}0$ and $\text{8}0$ . $\left(\text{L}0\text{ 16}-\text{2}\right)$
a. Show that the range of S is $\text{5}0$ while that of P is $\text{3}0$ 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?
c. What is the present value of the portfolio?
d. Given that the stock currently is selling at $\text{1}00$ , show that the value of the put must be $\text{1}0.\text{91}$ .