IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates
Continuously compounded spot rates are 4% for 1 year and 5% for 2 years. What is the continuously compounded forward rate for the year from time 1 to time 2?
The forward rate for year two is 6%. Under continuous compounding, the two-year spot rate times two, which is 10%, minus the one-year spot rate times one, which is 4%, gives 6% over the single year between times one and two.
- A4.5%
- B5.0%
- C5.5%
- D6.0%Correct
- 9.0%
Explanation
Forward rate = (2×5% − 1×4%)/(2−1) = 10% − 4% = 6%. Option A is the simple average of the spot rates, which ignores the longer holding period weighting.
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