Problem 3. (Replicating a stock with forwards and risk-free bonds, 16') In the lecture, we priced stock forwards by replicating a forward with stocks and risk-free bonds. In this problem, you will price forwards by replicating a stock with forwards and risk-free bonds. Suppose the stock does not pay dividends. Denote the dates for today and the expiration date are 0 and T respectively. Denote the current spot price of the stock as $0, the spot price at the expiration date is ST, and the forward price for time T settlement signed today is Forr- Assume the risk-free interest rate is a known constant r. Answer the following questions: (a). What are the cash ows for buying a stock (and then hold it and sell it at T)? Show the cash ow tables. Show the payoff diagram. (4') (b). What is the replicating portfolio of buying a stock that consists of certain positions in forwards and risk-free bonds (or equivalently, risk-free borrowing or lending)? Show the cash ow tables. Show the payoff diagrams of your chosen positions of forwards and risk-free bonds respectively, and then show the payoff diagram of the replicating portfolio. (8') (c). What are the costs of the two strategies, respectively? (2') ((1). Use the no-arbitrage principle to price the forward. (2')