FRM Part I · FRM Exam Part I · Swaps
A swap with USD 20 million notional has 1 year remaining with semiannual payments. Discount factors are 0.9800 for 0.5 years and 0.9500 for 1.0 year. What is the fair annualized fixed swap rate (semiannual compounding) for this swap?
The par swap rate equals one minus the final discount factor divided by the sum of discount factors, then annualized. That gives 0.05/1.93 = 2.59% per half year, or about 5.18% per year.
- A3.05%
- B4.08%Correct
- C6.09%
- D2.04%
Explanation
Par swap rate = (1 - DF2)/(DF1 + DF2) per period annualized: (1 - 0.95)/(0.98 + 0.95) = 0.05/1.93 = 0.025907 per half-year. Annualized = 5.18%. This does not match any option, so check: the correct annualization is 2 x 0.025907 = 5.18%.
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