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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates

Annual effective spot rates are 3% (one year), 4% (two years) and 5% (three years). What is the three-year par yield for a bond paying annual coupons?

The three-year par yield is 4.93%. It is (1 − v3) divided by the sum v1 + v2 + v3, which is 0.136162/2.759268. Because the spot curve slopes upward, the par yield falls below the 5% three-year spot rate.

  1. A4.93%Correct
  2. B5.00%
  3. C4.00%
  4. D5.25%
  5. 7.18%

Explanation

v1 = 0.970874, v2 = 0.924556 and v3 = 0.863838, so the sum is 2.759268. The par yield is (1 - v3)/(v1 + v2 + v3) = 0.136162/2.759268 = 4.93%. Dividing by 3·v3 gives 5.25%, which discounts all coupons at the three-year rate. Dividing by (v1 + v2) gives 7.18%, which omits the final coupon from the annuity.

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