IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates
The one-year par yield is 4% and the two-year par yield is 5%, both annual effective with annual coupons and redemption at par. What is the two-year spot rate, to two decimal places?
The two-year spot rate is 5.03%. The one-year spot equals the one-year par yield of 4%. Pricing the two-year par bond at par gives the two-year discount factor 0.9066, and converting that to an annual rate gives about 5.03%, slightly above the par yield.
- A5.00%
- B5.03%Correct
- C5.10%
- D5.25%
- 4.51%
Explanation
The one-year spot rate equals the one-year par yield, 4%, so v1 = 0.961538. For the two-year par bond, 1 = 0.05 v1 + 1.05 v2, giving v2 = (1 - 0.048077)/1.05 = 0.906593. Then s2 = (1/0.906593)^0.5 - 1 = 5.03%. Taking 5.00% treats the par yield as the spot rate, which ignores that the first coupon is discounted at 4%.
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