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

A practitioner observes that historical changes in short rates show larger absolute moves when rates are high than when rates are low, and that rates rarely go below zero in the sample. Which model feature best matches this evidence?

Volatility that rises with the level of the rate, as in lognormal or square-root models, fits the evidence. It produces bigger absolute moves at high rates and shrinking moves near zero, which helps keep rates from going negative.

  1. AConstant basis-point volatility with a normal distribution
  2. BVolatility that increases with the level of the rate, as in lognormal or square-root modelsCorrect
  3. CZero volatility with a time-varying drift only
  4. DVolatility that decreases as the rate rises

Explanation

Larger absolute moves at higher rates imply level-dependent volatility, and the near absence of negative rates suggests volatility declines as rates approach zero. Lognormal or square-root specifications deliver both. Constant volatility ignores the level effect, and decreasing volatility contradicts the observation.

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