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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

Zero-coupon bond prices today are P(0,1)=0.95 and P(0,2)=0.89. What is the one-year forward rate for the period from time 1 to time 2, expressed as an annual effective rate (to 2 decimal places)?

The forward rate from time 1 to 2 is P(0,1)/P(0,2) − 1 = 0.95/0.89 − 1, which is about 6.74% per annum. This follows because investing to time 2 must give the same result as rolling over at the forward rate.

  1. A6.30%
  2. B6.74%Correct
  3. C5.26%
  4. D6.00%
  5. 5.00%

Explanation

Forward accumulation = P(0,1)/P(0,2) = 0.95/0.89 = 1.06742, so the forward rate is 6.74%. Option 6.30% would come from using 0.89/0.95 incorrectly inverted differently, and 6.00% simply subtracts prices.

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