5. We will derive a two-state put option value in this problem. The initial stock price is $100, the strike price is $110, the risk-free interest rate is *rf = 10%, and the two possibilities for the nal price of the stock at expiration are $130 and $80. (a) What is the range of possible values for the stock and for the put at expiration? Find the hedge ratio of the put. (b) Form a portfolio that guarantees a certain payoff, constructed from a combination of shares of stock and puts. What is the payoff of this portfolio at expiration? (c) What is the present value of this portfolio? (d) Given that the stock currently sells for $100, nd the value of the put today