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

Continuously compounded spot rates are 4.0% for two years and 4.5% for three years. What is the implied continuously compounded forward rate for the period between year 2 and year 3?

The implied forward rate between years 2 and 3 is 5.5%. Continuous compounding makes total yield additive, so the forward equals 3 times 4.5% minus 2 times 4.0%, divided by the one-year gap. This gives 13.5% minus 8.0%, or 5.5%.

  1. A4.25%
  2. B4.50%
  3. C5.50%Correct
  4. D6.50%

Explanation

With continuous compounding, f = (3×4.5% − 2×4.0%)/(3 − 2) = (13.5% − 8.0%)/1 = 5.5%. Check: e^(0.08)·e^(0.055) = e^(0.135) = e^(3×0.045). The 4.50% option wrongly uses the three-year spot as the forward rate.

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