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

A practitioner notes that a Gauss+ model's Gaussian factors can imply negative short rates. Which statement about this feature is most accurate?

Negative short rates are a recognized limitation of Gaussian dynamics, since a normal distribution always gives some probability to negative values. Practitioners often accept this for tractability when rates are well above zero, because the probability is then small. Mean reversion does not prevent it.

  1. AIt is a limitation of Gaussian dynamics, and in practice is often accepted because the probability is small when rates are well above zeroCorrect
  2. BIt is impossible because mean reversion forces rates to stay positive
  3. CIt arises only when factors are perfectly correlated
  4. DIt means the model cannot price zero-coupon bonds

Explanation

Normally distributed rates always assign some probability to negative values. The probability depends on the level and volatility and is often small when rates are high, so practitioners may accept it for tractability. Mean reversion does not bound rates at zero.

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