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FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

In the Vasicek model dr = k(θ - r)dt + σdW, an analyst describes the parameter θ. Which description is correct?

θ is the long-run level toward which the short rate is pulled. The parameter k sets how fast the rate reverts, and σ sets its volatility, so only the long-run level description fits θ in the Vasicek drift.

  1. AThe long-run level toward which the short rate is pulled in the risk-neutral processCorrect
  2. BThe speed at which the short rate reverts to its mean
  3. CThe annualized volatility of the short rate
  4. DThe market price of interest rate risk

Explanation

In the stated dynamics θ is the long-run mean level of the short rate and k controls the speed of reversion. The speed description fits k, and the volatility description fits σ. None of these belongs to θ.

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