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

The Salomon Brothers (lognormal) model in the reading is one in which the short rate's volatility is proportional to the rate, and a practitioner observes that market data show basis-point volatility is roughly constant at low rates but the lognormal model scales it with level. Which is the main practical drawback of a purely lognormal model when rates are very low?

A purely lognormal model makes basis-point volatility proportional to the rate, so when rates are very low that volatility shrinks toward zero. This can understate the volatility actually observed in markets, even though the model keeps rates positive.

  1. AIt permits negative rates
  2. BIt implies basis-point volatility becomes very small at low rates, which may understate observed volatilityCorrect
  3. CIt cannot be calibrated to the initial term structure
  4. DIt implies infinite volatility at zero rates

Explanation

With volatility proportional to r, as r falls toward zero the basis-point volatility shrinks toward zero, often below what is observed in practice. The lognormal model does keep rates positive, so A is wrong; calibration to the curve is possible via time-dependent drift, and volatility goes to zero, not infinity.

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