Question

1. Suppose that the exchange rate (spot price) of Euro in GBP (British Pound) is GBP 0.95.   In addition, assume that you can freely borrow and lend in GBP for any maturity at a rate of 2% per annum and that you can do the same in Euro at a rate of 1% per annum. Both rates are continuously compounded rates. Given these assumptions:

1. Compute the forward price (exchange rate) of the GBP in Euro for delivery of the GBP in one year.
2. Compute the forward price (exchange rate) of the Euro in GBP for delivery of the Euro in one year.

2. Given the same information as in question 6 above, you realize, when you call your bank, that the forward price (exchange rate) of the GBP in Euro for delivery in one year is Euro 1.1. Present a trade which will let you lock in an arbitrage profit by buying or selling GBP spot and/or forward, borrowing or lending money in the Euro interest rate markets, and borrowing or lending in the GBP interest rate markets.

Answer 1

a]

for this part, GBP is the foreign currency and Euro is the domestic currency

spot exchange rate of GBP in Euro is 1/0.95 = 1.0526

f = s * ((1 + I_d)/(1 + I_f))^n , where

f = forward exchange rate (in terms on number of units of domestic currency per unit of foreign currency)

s = spot exchange rate (in terms on number of units of domestic currency per unit of foreign currency)

I_d = domestic interest rate

I_f = foreign interest rate

n = number of time periods

f = 1.0526 * ((1 + 0.01)/(1 + 0.02))^1

f = 1.0423

b]

f = s * ((1 + I_d)/(1 + I_f))^n , where

f = forward exchange rate (in terms on number of units of domestic currency per unit of foreign currency)

s = spot exchange rate (in terms on number of units of domestic currency per unit of foreign currency)

I_d = domestic interest rate

I_f = foreign interest rate

n = number of time periods

f = 0.95 * ((1 + 0.02)/(1 + 0.01))^1

f = 0.9594

Arbitrage trade]

the forward exchange rate of GBP in Euro should be 1.0423 as per the interest rates

however bank rate is 1.1. that means the bank rate is overpriced

to make an arbitrage profit, these steps are to be taken :

• borrow money in Euros
• convert the money into GBP at the spot exchange rate
• invest the GBP money at the GBP risk free rate of 2%
• at the end of 1 year, convert the investment proceed back into Euro at the forward exchange rate of 1.1