Question #27
Reading: Reading 30 Pricing and Valuation of Forward Commitments
PDF File: Reading 30 Pricing and Valuation of Forward Commitments.pdf
Page: 12
Status: Unattempted
Question
Consider a fixed-for-fixed 1-year $100,000 semiannual currency swap with rates of 5.0% in USD and 4.8% in CHF, originated when the exchange rate is $0.34. After the first settlement, the exchange rate is $0.35 and the term structure is: 90 days 180 days MRR 5.2% 5.6% Swiss 4.8% 5.4% What is the value of the swap to the USD payer?
Answer Choices:
A. $2,814
B. $2,937
C. -$2,719
Explanation
CHF periodic coupon (per 1 CHF) = 0.048/2 = 0.024
DF for 180 day CHF = 1 / (1 + 0.054 × (180/360)) = 1/1.027 = 0.9737
PV of CHF cash flows (per 1 CHF) = 0.9737 × 1.024 = 0.9971
At the current exchange rate the value is 0.9971 × 0.35 = USD 0.3490
The notional amount is 100,000/0.34 = 294,118 CHF so the dollar value of the CHF
payments is 0.3490 × 294,118 = $102,647.
USD periodic coupon (per 1 USD) = 0.05/2 = 0.025
DF for 180 day USD = 1 / (1 + 0.056 × (180/360)) = 1/1.028 = 0.9728
PV of USD cash flows (per 1 USD) = 0.9728 × 1.025 = 0.9971
Value (for notional = $100,000) = 0.9971 × 100,000 = $99,710.
The value of the swap to the dollar payer is 102,647 - $99,710 = $2,937.