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FRM Part I · FRM Exam Part I · Swaps

A currency swap has one year remaining with a single final payment. The party receives GBP 4% on GBP 10 million and pays USD 4% on USD 13 million, with principals exchanged at maturity. Spot is USD 1.30 per GBP. Annual-compounded yields are 3% in GBP and 4% in USD. Using the present value of the GBP bond converted at spot, what is the swap's value to the party in USD?

The swap is worth about plus USD 0.126 million to the party. The GBP bond it receives is worth GBP 10.097 million, or USD 13.126 million at spot, while the USD bond it pays is worth exactly USD 13.0 million at par, leaving a gain of USD 0.126 million.

  1. A+USD 0.126 millionCorrect
  2. B+USD 0.131 million
  3. C-USD 0.126 million
  4. D+USD 0.097 million

Explanation

GBP bond: 10.4/1.03 = GBP 10.0971m, which is USD 13.1262m at spot. USD bond: 13.52/1.04 = USD 13.0m, which is par. Value = 13.1262 - 13.0 = +USD 0.126m. As a check, the forward rate is 1.30 × 1.04/1.03 = 1.3126, so 10.4 × 1.3126 - 13.52 = 0.1313 at maturity, and discounting at 4% gives 0.126. The 0.131 option is that undiscounted figure. The 0.097 option is the value in GBP, not USD.

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