(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 S0, the spot price at the

expiration date is ST, and the forward price for time T settlement signed today is F0,T.

Assume the risk-free interest rate is a known constant r.

Answer the following questions:

(a). What are the cash flows for buying a stock (and then hold it and sell it at T)? Show the

cash flow 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 zero-coupon bonds (or equivalently, risk-free borrowing or lending)?

Show the cash flow 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)

(d). Use the no-arbitrage principle to price the forward. (2)