Question

The original question and answers are shown below, but my question is how do we get the value:Pound0.98 when answering the part B question?

Assume a forward contract on pound sterling. Suppose the spot exchange rate is $1.60/pound. Suppose the three month interest rate on dollar is 6% while the three month interest rate on pound is 8%, both continuous compounding terms. What is the arbitrage free three month forward rate?

(a) What is the arbitrage free forward price?
(b) Suppose the delivery price of the forward contract differed from answer in (a) and instead let F = $1.615. Explain the arbitrage strategy one should follow? Explain your answer in detail.
Answer:
(a) We have: r= 0.06, rf=0.08, t = 3 which means ¼ year, Spot = $1.60/Pound.
The theoretical price (arbitrage free) forward price is:
F = (exp)^[(0.06-0.08)(1/4)] x ($1.60) = $1.592

(b) If F = $1.615 means forward is overpriced relative to spot so we should sell forward and buy spot to create riskless profit. We must set out our arbitrage profit clearly.

The Arbitrage strategy:
- Enter into short forward contract to deliver one pound for $1.615 in three months.
- Buy Pound[Exp^-(rf*t)]=Pound0.98 at the spot price of $1.60/Pound
- Finance the spot purchase by borrowing (0.98)x(1.60) = $1.568 for three months at the dollar interest rate of 6%.
- Invest Pound0.98 for three months at the sterling interest rate of 8%.

Answer 1

0.98 = e^(-0.08/4)

Basically, you have to raise the exponential to a quarter of risk free rate ( 3 months = 1 quarter)