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

A risk manager notes that in a lognormal short-rate model, as the current rate level falls from 6% to 1% with constant proportional volatility, what is the implication for the model's calibration to the market?

Because basis-point volatility equals σ times the rate, it shrinks sharply as rates fall from 6% to 1%. If real-market basis-point volatility stays fairly stable at low rates, the lognormal model understates rate risk there.

  1. ABasis-point volatility falls sharply, so the model may understate rate moves if markets show stable basis-point volatility at low ratesCorrect
  2. BBasis-point volatility rises sharply, so the model overstates risk at low rates
  3. CBasis-point volatility is unchanged, so the model fits any rate level equally
  4. DThe model forces rates to become negative, making low-rate risk undefined

Explanation

With basis-point volatility = σ·r, dropping r from 6% to 1% cuts it to one-sixth. If observed basis-point volatility stays relatively stable at low rates, the lognormal model understates risk. Rates never go negative in this model.

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