FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
An analyst calibrates the Vasicek mean-reversion speed to k = 0.35 per year using historical short-rate data. What is the half-life of a deviation of the short rate from its long-run mean, in years?
The half-life is about 1.98 years. A deviation from the mean decays as e^(−kt), so it halves when t = ln2/k = 0.6931/0.35. The value 1/k (2.86 years) is a different measure, namely the time to fall to roughly 37% of the initial gap.
- A1.98Correct
- B2.86
- C0.24
- D0.50
Explanation
The deviation decays as e^(−kt), so the half-life solves e^(−kt) = 0.5, giving t = ln2/k = 0.693147/0.35 = 1.98 years. The figure 2.86 is 1/k, the time for the deviation to fall to about 37%, not 50%. The figure 0.24 multiplies ln2 by k instead of dividing.
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