Question

an interest only currency swap has a remaining life of 2 years it involves exchanging interest at 14 percent on 20 million pounds for interest at 10 percent on 14 million dollars once a year the term structure of interest rates is currently flat in both the us and the uk if the swap were negotiated today the interest rates exchange would be $8% and pound11% all rates were quoted with annual compounding the current exchange rate is $ 1.95=1.00 euro. what is the value of the swap to the party paying in dollars?

Answer 1

Dollar Leg of Swap:

Principal = $ 14 million and Interest Rate = 10 %

Current Interest in $ = 8 %

Annual Interest = 0.1 x 14 = $ 1.4 million

PV of Annual Interest today (at t=0) = I1 = 1.4 / (1.08) + 1.4 / (1.08)^(2) = $ 2.4966 million

Pound Leg of Swap:

Principal = £ 20 million and Interest Rate = 14 %

Current Interest in £ = 11 %

Annual Interest = 0.14 x 20 = £ 2.8 million

PV of Annual Interest today (at t=0) = I2 = 2.8 / (1.11) + 2.8 / (1.11)^(2) = £ 4.7951 million

Current Exchange Rate = $ 1.95 = £ 1

I2 in $ terms = 4.7951 x 1.95 = $ 9.3504

Value of Swap to Dollar Payer = I2 in $ - I1 = 9.3504 - 2.4966 = $ 6.8538 million or $ 6.85 million approximately.