- CFA Exams
- CFA Level I Exam
- Topic 7. Derivatives
- Learning Module 33. Pricing and Valuation of Forward Commitments
- Subject 9. Currency Swap Contracts
CFA Practice Question
Consider a one-year currency swap with semi-annual payments. The two currencies are the US$ and the euro. When the two parties entered the swap, the exchange rate was $0.75/euro, and the term structure was as follows:
The annualized fixed rates in dollars and euros are 7.84% and 6.48%, respectively.
Ninety days after the swap, the term structure is as follows:
If the current exchange rate is 0.7, what is the market value of the swap to pay dollar-fixed and receive euro-fixed?
A. -0.0712
B. -0.0661
C. 0.0698
Explanation: First we compute the dollar discount factors:
B90(180) = 1 / (1 + 0.071 x 90/360) = 0.9826
B90(360) = 1 / (1 + 0.074 x 270/360) = 0.9474
The present value of the fixed dollar payments of 0.0392 (0.0784/2), including the hypothetical notional principal, is 0.0392 x (0.9826 + 0.9474) + 1 x 0.9474 = $1.0231.
The 180-day dollar rate at the start of the swap was 7.2%, so the first floating dollar payment would be 0.036. The present value of the floating payments plus the hypothetical notional principal of $1 is 1.036 x 0.9826 = $1.0180.
B90euro(90) = 1 / (1 + 0.055 x 90/360) = 0.9864
B90euro(270) = 1 / (1 + 0.06 x 270/360) = 0.9569
The present value of the fixed payments plus the hypothetical 1 euro notional principal is 0.0324 x (0.9864 + 0.9569) + 1 (0.9569) = 1.0199 euro.
The 180-day euro rate at the start of the swap was 6%, so the first floating euro payment would be 0.03. The present value of the floating payments plus the hypothetical notional principal of 1 euro is 1.03 x 0.9864 = 1.0160 euro.
B90(180) = 1 / (1 + 0.071 x 90/360) = 0.9826
B90(360) = 1 / (1 + 0.074 x 270/360) = 0.9474
Fixed dollar payments:
The present value of the fixed dollar payments of 0.0392 (0.0784/2), including the hypothetical notional principal, is 0.0392 x (0.9826 + 0.9474) + 1 x 0.9474 = $1.0231.
Floating dollar payments:
The 180-day dollar rate at the start of the swap was 7.2%, so the first floating dollar payment would be 0.036. The present value of the floating payments plus the hypothetical notional principal of $1 is 1.036 x 0.9826 = $1.0180.
Then we compute the euro discount factors:
B90euro(90) = 1 / (1 + 0.055 x 90/360) = 0.9864
B90euro(270) = 1 / (1 + 0.06 x 270/360) = 0.9569
Fixed euro payments:
The present value of the fixed payments plus the hypothetical 1 euro notional principal is 0.0324 x (0.9864 + 0.9569) + 1 (0.9569) = 1.0199 euro.
Floating euro payments:
The 180-day euro rate at the start of the swap was 6%, so the first floating euro payment would be 0.03. The present value of the floating payments plus the hypothetical notional principal of 1 euro is 1.03 x 0.9864 = 1.0160 euro.
The euro notional principal, established at the start of the swap, is 1/0.75 = 1.3333 euro.
Now we obtain the following values for the four swaps:
- Pay dollar fixed, receive euro fixed = -$1.0231 + euro 1.3333 x $0.7 x 1.0199 = -$0.0712
- Pay dollar fixed, receive euro floating = -$1.0231 + euro 1.3333 x $0.7 x 1.0160 = -$0.0749
- Pay dollar floating, receive euro fixed = -$1.0180 + euro 1.3333 x $0.7 x 1.0199 = -$0.0661
- Pay dollar floating, receive euro floating = -$1.0180 + euro 1.3333 x $0.7 x 1.0160 = -$0.0698
User Contributed Comments 3
| User | Comment |
|---|---|
| Yurik74 | What is the reason to calculate floating rate payments? Just for illustration, I guess? |
| dblueroom | yeah two of my favorite currency and swap, they're highly likely to be on the exam, no kidding! |
| jazzguitar | You have to calculate the floating rate payments as the next floating rate payment "isn't floating any more". It's rather being determined by the last value of the reference rate. If it was the actual value, the value of the floating rate side would of course be always 1 (which is not the case above!) |