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

A risk manager observes that historically, basis-point volatility of short rates has been much lower when rates are near zero than when rates are at 8%. Which modeling choice is most consistent with this empirical pattern?

A lognormal-type model, where volatility is proportional to the rate level, fits the observation because basis-point volatility is small at low rates and large at high rates. A constant-volatility normal model cannot reproduce this level dependence.

  1. AA constant-volatility normal model, because it fixes basis-point volatility
  2. BA model where volatility is proportional to the rate level, such as a lognormal modelCorrect
  3. CA model with deterministic drift and zero volatility
  4. DA model where volatility declines as rates rise

Explanation

Basis-point volatility rising with the rate level is what a lognormal (proportional volatility) specification delivers, while a normal model assumes the same basis-point volatility at all levels. Declining volatility with higher rates is the opposite of the observation.

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