FRM Part I · FRM Exam Part I · Swaps
Zero rates (annually compounded) are 2.00% for 1 year and 3.00% for 2 years. What is the par swap rate for a 2-year annual-pay swap, rounded to two decimals?
The par swap rate is about 2.99%. Discount factors are 0.9804 for one year and 0.9426 for two years, and the par rate equals one minus the final discount factor divided by the sum of discount factors, giving 0.0574 divided by 1.9230, or roughly 2.99%.
- A2.50%
- B2.99%Correct
- C3.00%
- D2.01%
Explanation
d1 = 1/1.02 = 0.980392. d2 = 1/1.03^2 = 0.942596. Par rate = (1 - d2)/(d1 + d2) = 0.057404/1.922988 = 2.985%, about 2.99%. The simple average 2.50% ignores weighting by discount factors; 3.00% is just the 2-year zero rate.
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