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

A risk manager is calibrating a Vasicek model in an environment where the current short rate is 0.5% and the long-run mean is 1.5%. A colleague asks whether the model can generate negative short rates. Which statement is correct?

Vasicek can produce negative short rates. Its short rate is normally distributed with constant volatility, so there is always some probability of a negative outcome at any horizon. Mean reversion pulls the expected rate toward a positive mean but does not impose a floor at zero.

  1. AYes; because the short rate is normally distributed, there is a positive probability of negative rates at any horizon.Correct
  2. BNo; mean reversion toward a positive θ prevents the short rate from ever falling below zero.
  3. CNo; the volatility of the short rate shrinks proportionally as the rate approaches zero.
  4. DYes, but only if the mean-reversion speed k is set to zero.

Explanation

In Vasicek, volatility is constant and the short rate is normally distributed, so negative rates have a positive probability regardless of θ or k. Mean reversion only pulls the expected rate toward θ. Volatility proportional to the rate level is a feature of CIR-type models, not Vasicek.

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