1. A six-month long forward contract on 1,000 barrels of Brent Crude Oil is entered into when the commodity price is $57.14 per barrel and the interest rate is 5% per annum with continuous compounding.
(a) What is the forward price at the date of entry?
(b) Three months later, the price of Brent Crude Oil is $59.63 per barrel (the interest rate is unchanged). What is the present forward price and the present value of the original long forward contract?
(c) Suppose one agrees to enter into a six-month forward contract on 1,000 barrels of Brent Crude Oil with the forward price $60,000 when the price of one barrel is $57.14. By way of "mental experiment", create a series of trades to show the arbitrage opportunity this will create.
2. Suppose the fixed interest rates in the UK and Euro Zone are 5% and 2% per annum respectively, with continuous compounding. Also, assume that in the Euro market the current Sterling exchange rate is 1.4917 euros (so that 1,000 sterlin pounds costs 1,491.7 euros). What is the fair futures price in the Euro Zone for a contract on 1,000 sterling pounds deliverable in three months? (Assume that a futures contract is the same as a forward.)
3. The risk-free fixed rate of interest is 6% per annum with continuous compounding,and the dividend yield on a share of an XYZ company is 3.5% per annum with continuous compounding (i.e. the asset pays continuously compounded interest on its instant price). The current value of the share is $200. What is the six-month forward price for one share of this type?