FRM Part I · FRM Exam Part I · Swaps
A 2-year annual-pay swap is priced off projected floating rates of 3% for year 1 and 5% for year 2. Discounting uses OIS discount factors of 0.97 (1 year) and 0.93 (2 years). What is the par swap rate, to two decimals?
The par swap rate is the discount-factor-weighted average of the projected floating rates: (3% times 0.97 plus 5% times 0.93) divided by 1.90, which equals 3.98%. A simple average of 4% overweights the later, higher forward rate, and the reversed weighting overstates it.
- A3.98%Correct
- B4.00%
- C4.02%
- D3.00%
Explanation
The par rate equates the PV of fixed payments to the PV of projected floating payments: (0.03 x 0.97 + 0.05 x 0.93) / (0.97 + 0.93) = (0.0291 + 0.0465) / 1.90 = 0.0756 / 1.90 = 3.98%. A simple average of forwards (4.00%) ignores that the earlier cash flow carries a higher discount factor. Reversing the weights gives 4.02%. Using only the first-year rate gives 3.00%.
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