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FRM Part I · FRM Exam Part I · Swaps

A firm has two years left on a fixed-for-fixed currency swap with annual payments. It receives EUR 3% on a EUR 10 million principal and pays USD 5% on a USD 11 million principal, with principals exchanged at maturity. The spot rate is USD 1.10 per EUR. Flat annual-compounded yields are 3% in EUR and 4% in USD. What is the swap's value to the firm, in USD?

The swap is worth about minus USD 0.207 million to the firm. The received EUR bond is worth par, USD 11.0 million, while the USD bond it pays is worth about USD 11.2075 million at a 4% yield, so the firm is paying an above-market 5% coupon.

  1. A-USD 0.207 millionCorrect
  2. B+USD 0.207 million
  3. C-USD 1.207 million
  4. D-USD 0.189 million

Explanation

The EUR bond has a 3% coupon and a 3% yield, so it is worth par: EUR 10m, or USD 11.0m. The USD bond is 0.55/1.04 + 11.55/1.0816 = 0.5288 + 10.6786 = USD 11.2075m. Value = 11.0 - 11.2075 = -0.207m. The +0.207 option has the sign reversed. The -1.207 option subtracts the EUR value without converting it to USD. The -0.189 option leaves the value in EUR.

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