FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
Under the Vasicek model dr = k(θ − r)dt + σdw, the current short rate is 2.00%, k = 0.50, and θ = 5.00%. Ignoring the volatility term, what is the expected change in the short rate over the next 0.10 years, using the drift over the small interval?
The expected change is k(θ − r)dt = 0.50 × (5% − 2%) × 0.10 = +0.15%. The rate is below the long-run mean, so the drift is positive and pulls the short rate upward.
- A+0.30%
- B+0.15%Correct
- C−0.15%
- D+1.50%
Explanation
Expected change = k(θ − r)dt = 0.50 × (5% − 2%) × 0.10 = 0.50 × 3% × 0.10 = 0.15%. The 0.30% option omits the 0.50 factor for k. The −0.15% option has the sign wrong, and 1.50% omits dt.
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