FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
In a Vasicek model, k = 0.25, θ = 6.00%, σ = 1.00%, and the current short rate is 4.00%. What is the expected change in the short rate over the next 0.5 years, using the drift over a small interval (dt = 0.5) as an approximation?
The expected change is +0.25%. The drift equals k times (θ minus r) times dt, which is 0.25 × 2% × 0.5. Because the current rate is below the long-run mean, the drift is positive and pulls the rate upward.
- A+0.25%Correct
- B−0.25%
- C+0.50%
- D+0.125%
Explanation
Drift = k(θ − r)dt = 0.25 × (6% − 4%) × 0.5 = 0.25%. The rate is below θ so the change is positive. Using 0.25 × 2% without dt gives 0.50%, which ignores the time interval. Halving again gives 0.125%, a miscomputation.
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