Question

Suppose that the term structure of interest rates is flat in England and Germany. The GBP interest rate is 6% per annum and the EUR rate is 4% per annum. In a swap agreement, a financial institution pays 10% per annum in GBP and receives 8% per annum in EUR. The exchange rate between the two currencies has changed from 1.1 EUR per GBP to 1.05 EUR per GBP since the swap’s initiation. The principal in British pounds is 10 million GBP. Payments are exchanged every year, with one exchange having just taken place. The swap will last three more years. What is the value of the swap to the financial institution in terms of euros? Assume all interest rates are continuously compounded.

Answer 1

The Swap can be valued in terms of Bonds

Value of Swap for Financial Institution (in EURO)

= Value of Bond in EUR - Value of Bond in GBP*current Exchange rate

The Financial Institution pays 10% in GBP and receives 8% in EUR and at the end of 3 years the notional principal is also exchanged

Notional principal =10 million GBP = 10*1.1 = 11 million EUR (at the time of initiation of Swap, Principal is equal)

Annual payment made by the Institution= GBP 10 million * (exp(0.1)-1)= GBP 1.051709 million for the next 3 years and GBP 10 million at the end of 3 years

So, value of the GBP bond = 1.051709*exp(-0.06*1)+1.051709*exp(-0.06*2)+1.051709*exp(-0.06*3)+10*exp(-0.06*3)

= 11.15441 million GBP

Similarly , annual EUR payment received = 11 million * (exp(0.08)-1) = EUR 0.9161577 million for the next 3 years and EUR 11 million received at the end of 3 years

So, value of the EUR bond

= 0.9161577*exp(-0.04*1)+0.9161577*exp(-0.04*2)+0.9161577*exp(-0.04*3)+11*exp(-0.04*3)

= 12.294639 million EUR      

Value of Swap for Financial Institution in EURO

= 12.294639 - 11.15441*1.05

=0.58251006 million EURO or 582510.06 Euro