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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution

In the Vasicek model dr = k(θ − r)dt + σdW, a risk analyst notes that the short rate is currently well above θ. Which statement best describes the effect of the parameter k on the expected path of the rate?

A larger k means faster mean reversion: the expected short rate closes the gap to the long-run level θ more quickly, as seen in the term e^(−kt). It does not change θ itself or the volatility parameter σ, and the Vasicek rate can still be negative.

  1. AA larger k makes the expected rate return to θ more quicklyCorrect
  2. BA larger k raises the long-run level to which the rate converges
  3. CA larger k increases the instantaneous volatility of the rate
  4. DA larger k makes the rate follow a geometric process that cannot go negative

Explanation

In Vasicek the expected rate is θ + (r0 − θ)e^(−kt), so k is the speed of mean reversion. A larger k shrinks the gap to θ faster. The long-run level is θ, and volatility is governed by σ, so the other statements are wrong.

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