FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution
In Model 1 with constant drift λ = 0.20% per year and σ = 1.00% per year, the current short rate is 3.00%. What is the mean and standard deviation of the short rate in 4 years?
The mean is 3.80% because the 3.00% starting rate plus 0.20% drift for four years gives 3.80%. The standard deviation is 2.00% because volatility scales with the square root of time, 1.00% times √4.
- AMean 3.80%, standard deviation 2.00%Correct
- BMean 3.80%, standard deviation 4.00%
- CMean 3.20%, standard deviation 2.00%
- DMean 3.80%, standard deviation 1.00%
Explanation
Mean = 3.00% + 0.20% × 4 = 3.80%. Standard deviation = σ√T = 1.00% × √4 = 2.00%. Using σ×T gives 4.00%, which wrongly scales volatility linearly in time; omitting the drift gives 3.20%/3.00%.
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