Skip to content

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

A risk analyst compares two one-factor short-rate models. Model A assumes dr = λ(t)dt + σ dw with constant σ. Model B assumes dr = λ(t)dt + σ r dw. Which statement about the two models is correct?

The normal model with constant basis-point volatility allows negative rates, while the lognormal model, whose volatility is proportional to the rate, keeps rates positive. Volatility shrinking toward zero as the rate falls prevents the rate from crossing zero.

  1. AModel A (normal) permits negative short rates, whereas Model B (lognormal) keeps rates positiveCorrect
  2. BModel A keeps rates positive, whereas Model B permits negative rates
  3. CBoth models permit negative rates because both include a Brownian motion term
  4. DNeither model permits negative rates because both have a time-varying drift

Explanation

With constant volatility, the rate's changes are normally distributed, so the rate can become negative. In the lognormal model, the shock scales with r, so volatility shrinks as r approaches zero and r stays positive. The other options misattribute the property to the drift or to the Brownian term alone.

Did you get it right without looking?

One question tells you little. A timed set on The Art of Term Structure Models: Volatility and Distribution shows your real accuracy, how long you take and where you lose marks.

Practise The Art of Term Structure Models: Volatility and DistributionFree diagnostic mock

More The Art of Term Structure Models: Volatility and Distribution questions