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

A model validation team reviews a one-factor Vasicek implementation used to price zero-coupon bonds in a low-rate environment. Which statement about the model is correct?

The correct statement is that the short rate is normally distributed, so negative rates are possible. Vasicek has constant volatility and a linear mean-reverting drift, which gives Gaussian rates. This is a known limitation, but it is not wrong in a low-rate environment. Lognormal or level-proportional volatility belongs to other models.

  1. AThe short rate is normally distributed, so the model permits negative ratesCorrect
  2. BThe short rate is lognormal, so it can never fall below zero
  3. CThe volatility of rate changes is proportional to the level of the short rate
  4. DThe speed of mean reversion k has no effect on the volatility of long-maturity yields

Explanation

Vasicek has a constant σ and a linear mean-reverting drift, so the short rate is normally distributed and can be negative. That is a known drawback but useful when rates are near zero. A lognormal rate with proportional volatility describes models such as Black-Karasinski, not Vasicek. A higher k damps long-maturity yield volatility through B(T), so the last option is also wrong.

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