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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

Continuously compounded zero rates are 3.0% for 1 year and 4.0% for 2 years. What is the continuously compounded forward rate for the period from year 1 to year 2?

The forward rate is 5.00%. With continuous compounding, the 2-year rate is the time-weighted average of the first-year rate and the forward rate. So the forward equals 2×4% minus 1×3%, which is 5%, and the 2-year spot rate alone understates it.

  1. A5.00%Correct
  2. B4.00%
  3. C3.50%
  4. D6.00%

Explanation

With continuous compounding, f = (r2×T2 − r1×T1)/(T2 − T1) = (4.0%×2 − 3.0%×1)/1 = 5.00%. The 4.00% option is just the 2-year rate and ignores that the 2-year rate averages the first-year rate and the forward rate. The 3.50% option is the simple average of the two spot rates.

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