CFA Level I · CFA Level I Exam · Pricing and Valuation of Interest Rate and Other Swaps
A 3-year annual-pay swap is priced from a 1-year spot rate of 2.00%, a 1-year forward rate one year ahead of 3.00%, and a 1-year forward rate two years ahead of 4.00%. The swap fixed rate is closest to:
The swap fixed rate is about 2.98%. Build the discount factors from the spot and forward rates, then divide one minus the final discount factor by the sum of the factors. The simple average of the rates, 3.00%, overstates the result because it ignores the discount weights.
- A2.00%
- B2.98%Correct
- C3.00%
Explanation
The discount factors are Z1 = 1/1.02 = 0.98039, Z2 = 0.98039/1.03 = 0.95184 and Z3 = 0.95184/1.04 = 0.91523. The sum is 2.84746. The swap rate is (1 − 0.91523)/2.84746 = 2.98%. The simple average of the forward rates (3.00%) ignores that earlier cash flows carry larger discount weights.
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