MT3470/MT4570/MT5547: Problem Set 1
1. Explain briefly what is the difference between a long forward position and a short forward
position. [20]
2. An investor enters into a short cotton forward contract where the strike price is 50 pence per
kilo. The contract is for the delivery of 50 000 kilos. How much does the investor gain or lose
if the cotton price at the end of the contract is
(a) 48.20 pence per kilo;
(b) 51.30 pence per kilo? [20]
3. Consider a six-month forward contract on a non-dividend paying stock when the spot price is
£30 and the risk-free interest rate with continuous compounding is 12% per annum.
a) Calculate the forward price.
b) Suppose that the delivery price in the contract is equal to the forward price, i.e. K = F0,
so that the value of the contract is equal to zero at the outset. What will be the value of the
contract (for the holder of the long position) and the forward price three months later, if at
that time the stock price is equal to £34? [20]
4. Consider a one year forward contract on a stock with no income, when the spot price of the
stock is S(0) = £50 and the risk-free interest rate with continuous compounding is r = 10%
per annum.
a) Calculate the forward price F0.
b) Suppose a zero value forward contract with the same maturity and delivery price of F0 +£1,
is available on the same stock. Is there an arbitrage opportunity in this situation? If your
answer is yes, then describe an arbitrage strategy and, in particular, the risk-free profit.
c) Suppose a zero value forward contract with the same maturity and delivery price of F0−£1,
is available on the same stock. Is there an arbitrage opportunity in this situation? If your
answer is yes, then describe an arbitrage strategy and, in particular, the risk-free profit. [40]
[Total mark 100]
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