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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

A bank's treasury is calibrating a short-rate model for an environment in which rates are close to zero. Which statement about the models is most accurate?

Vasicek has constant basis-point volatility and normally distributed rates, so it can produce negative rates even with mean reversion. CIR volatility falls toward zero as the rate approaches zero, which keeps rates from turning negative, making it more suitable near zero.

  1. AThe Vasicek model can generate negative rates because its normally distributed shocks do not depend on the rate level, whereas CIR volatility shrinks as the rate approaches zero.Correct
  2. BThe CIR model can generate negative rates with the same probability as the Vasicek model because both have mean-reverting drift.
  3. CThe Vasicek model prevents negative rates because its drift pulls the rate toward a positive long-run mean.
  4. DThe CIR model has constant basis-point volatility, so it is unsuitable when the rate level is low.

Explanation

Vasicek has constant basis-point volatility and normally distributed rates, so negative rates are possible even with positive mean reversion. In CIR, volatility is proportional to √r and falls as r approaches zero, which restricts rates from going negative. The other statements reverse these properties.

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