FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
In the Vasicek model dr = k(θ − r)dt + σdw, a risk analyst is explaining the role of the parameter k to a portfolio manager. Which statement is correct?
In the Vasicek model, k is the speed of mean reversion. It scales the drift k(θ − r), so a larger k pulls the short rate back to the long-run mean θ faster. The mean is θ and volatility is σ.
- Ak is the speed of mean reversion; a larger k pulls the short rate back toward θ more quicklyCorrect
- Bk is the long-run volatility of the short rate
- Ck is the long-run mean level to which the short rate converges
- Dk is the risk premium demanded for bearing interest rate risk
Explanation
In the Vasicek model k governs how quickly the drift pulls r toward the long-run level θ. The long-run mean is θ, and volatility is σ. Confusing k with the mean or the volatility misreads the drift term k(θ − r).
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