Question

Suppose that the term structure of interest rates is flat in the US and UK. The USD interest rate is 2.5% per annum and the GBP rate is 2.9% p.a. Under the terms of a swap agreement, a financial institution pays 3% p.a. in GBP and receives 2.6% p.a. in USD. The principals in the two currencies are GBP20 million and USD32 million. Payments are exchanged every year, with one exchange having just taken place. The swap will last 3 more years NOTE: 1 USD = 0.8 GBP

i) Write out the formula for the valuation of a currency swap in terms of bond prices. From this formula, explain what prices and rates you need to calculate the value of a swap.

Answer 1

Using the above information, we can calculate the value of currency swaps in terms of bonds price as follows:

The US interest rate is 2.5% and the GBP rate is 2.9%

Interest rate for financial Institution is 2.6% received in US and 3% paid in GBP

Principal amount in USD is 32 Million and that of GBP is 20 Million

The swap involves exchanging the interest rates which are as below

USD interest = Principal Amount * Interest rate offered by financial Institution

= 32,000,000 * 2.6% = $ 0.832 million

GBP interest = Principal Amount * Interest rate

= 20,000,000 * 3% = GBP 0.60 million

Also 1 swap has already taken place and 3 swaps are pending.

The value of USD bond is calculated as below:

= (USD interest * Exp. value at rate of 2.5% for 1 year) + (Principal + Interest)* Exp value at rate of 2.5% for 3 years

=

= 0.832 * 0.9753 + (32.832) * 0.9277

= 0.811 + 30.46 = $ 31.27 Million = $ 31,270,000

The value of GBP bond is calculated as below:

= (GBP interest * Exp. value at rate of 2.9% for 1 year) + (Principal + Interest)* Exp value at rate of 2.9% for 3 years

=

= 0.60 * 0.9714 + ( 20.60) * 0.9167

= 0.583 + 18.88 = GBP 19.47 Million = GBP 19,470,000

So, value of swap in USD is

= (value of GBP bond * Exchange rate) - value of USD bond

= ( 19,470,000 * 1.25 ) - 31,270,000

= 24,337,500 - 31,270,000

= $ -6,932,500

Currency from GBP to USD = 1/0.80 = $ 1.25

Means 1GBP can be exchanged for $ 1.25.