1. In the absence of interest-rate uncertainty and delivery options, futures and forward prices must be the same. Does this mean the two contracts have identical cash- ow implications? (Hint: Suppose you expected a steady increase in prices. Would you prefer a futures contract with its daily mark-to-market or a forward with its single mark-to-market at maturity of the contract? What if you expected a steady decrease in prices?)
2. Consider a forward contract on a non-dividend-paying stock. If the term structure of interest rates is at (that is, interest rates for all maturities are the same), then the arbitrage-free forward price is obviously increasing in the maturity of the forward contract (i.e., a longer-dated forward contract will have a higher forward price than a shorter-dated one). Is this statement true even if the term-structure is not at?
3. The spot price of copper is $1.47 per lb, and the forward price for delivery in three months is $1.51 per lb. Suppose you can borrow and lend for three months at an interest rate of 6% (in annualized and continuously compounded terms).
(a) First, suppose there are no holding costs (i.e., no storage costs, no holding bene ts). Is there an arbitrage opportunity for you given these prices? If so, provide details of the cash cows. If not, explain why not.
(b) Suppose now that the cost of storing copper for three months is $0.03 per lb, payable in advance. How would your answer to Part (a) change? (Note that storage costs are asymmetric: you have to pay storage costs if you are long copper, but you do not receive the storage costs if you short copper.)
4. The SPX index is currently trading at a value of $1,265, and the FESX index (the Dow Jones EuroSTOXX Index of 50 stocks, referred to from here on as STOXX”) is trading at e3,671. The dollar interest rate is 3% , and the euro interest rate is 5%. The exchange rate is $1.28/euro. The six-month futures on the STOXX is quoted at e3,782. All interest rates are continuously compounded. There are no borrowing costs for securities.
(a) Compute the correct six-month forward futures prices of the SPX, STOXX, and the currency exchange rate between the dollar and the euro.
(b) Is the futures on the STOXX correctly priced? If not, show how to undertake an arbitrage strategy assuming you are not allowed to undertake borrowing or lending transactions in either currency.
5. The current level of a stock index is 450. The dividend yield on the index is 4% (in continuously compounded terms), and the risk-free rate of interest is 8% for six-month Sundaram & Das: Derivatives – Problems and Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 investments. A six-month futures contract on the index is trading for 465. Identify the arbitrage opportunities in this setting, and explain how you would exploit them. Get Finance Help Today
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