FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
In a Vasicek model, k = 0.25 per year, θ = 6%, and the current short rate is 2%. Ignoring volatility, what is the expected change in the short rate over the next 0.5 year using the instantaneous drift approximation (drift × time)?
The expected change is +0.50%. The annual drift is 0.25 times the 4% gap between the long-run mean and the current rate, which is 1.00% per year, and multiplying by half a year gives 0.50%.
- A+0.50%Correct
- B+1.00%
- C-0.50%
- D+2.00%
Explanation
Drift = k(θ - r) = 0.25 × (6% - 2%) = 1.00% per year. Over 0.5 year the expected change is 1.00% × 0.5 = 0.50%. Using the full year gives 1.00%, which ignores the time step.
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