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FRM Part I · FRM Exam Part I · Swaps

A company has two years left on a currency swap with annual payments. It receives GBP 4% on a GBP 10 million principal and pays USD 5% on a USD 15 million principal. The current spot rate is USD 1.50 per GBP. Flat annual-compounded discount rates are 3% for USD and 4% for GBP. What is the swap's value to the company in USD, using the bond approach?

The swap is worth about negative USD 0.57 million to the company. The GBP bond received is worth GBP 10 million, or USD 15.00 million. The USD bond paid is worth USD 15.57 million when discounted at 3%. The company receives the lower-valued bond, so the value is negative.

  1. A-USD 0.57 millionCorrect
  2. B+USD 0.57 million
  3. C-USD 5.57 million
  4. D-USD 0.28 million

Explanation

The GBP bond is valued at 4%, which equals its coupon, so it is worth GBP 10m, or USD 15.00m at spot. The USD bond is 0.75/1.03 + 15.75/1.0609 = 0.7282 + 14.8459 = USD 15.574m. The value to the company is 15.000 - 15.574 = -USD 0.574m. The -5.57 option wrongly compares GBP 10m with USD 15.574m without converting. The -0.28 option discounts USD at 4% instead of 3%.

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