FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
In a Vasicek model, σ = 1.2% per year and k = 0.3. Using the long-horizon variance σ²/(2k), what is the approximate stationary standard deviation of the short rate?
The stationary standard deviation is about 1.55%. It equals σ divided by the square root of 2k, so 1.2% divided by the square root of 0.6 gives roughly 1.55%, lower than σ because mean reversion limits how far rates wander.
- A1.55%Correct
- B0.72%
- C1.20%
- D2.19%
Explanation
Variance = σ²/(2k) = 0.000144/0.6 = 0.00024. The square root is about 1.549%, so 1.55%. Using σ²/k gives about 2.19%, which omits the factor of 2. Using σ alone ignores mean reversion.
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