Question

In a fixed-for-fixed currency swap, 3% on a US dollar principal of $150 million is received and 4% on a British pound principal of 100 million pounds is paid. The current exchange rate is 1.55 dollar per pound. Interest rates in both countries for all maturities are currently 5% (continuously compounded). Payments are exchanged every year. The swap has 2.5 years left in its life. What is the value of the swap?

Group of answer choices

−$7.15

−$8.15

−$9.15 ( Correct Answer)

−$10.15

Answer: C

The value of the British pound bond underlying the swap is in millions of pounds
4e-0.05×0.5+4e-0.05×1.5+104e-0.05×2.5 = 99.39
The value of the U.S. dollar bond is in millions of dollars
4.5e-0.05×0.5+4.5e-0.05×1.5+154.5e-0.05×2.5 = 144.91
The value of the swap is 144.91 – 99.39×1.55 = –9.15

Answer 1

British pound value of the bond in pounds
4e-0.05×0.5+4e-0.05×1.5+104e-0.05×2.5 = 99.39 (present value of all the cashflows discounted at continous rate of 5%)
U.S. dollar bond value is in millions
4.5e-0.05×0.5+4.5e-0.05×1.5+154.5e-0.05×2.5 = 144.91 ( similar approach. Finding present value of cashflows discounted at continous rate)

Value of swap= US bond value- British bond value*exchange rate
The value of the swap is 144.91 - 99.39×1.55 = -9.15 (option c)