Skip to content

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

A desk calibrates a Hull-White model by fitting σ(t) to cap volatilities. Compared with a constant-σ Model 3 calibrated to the same long-dated volatility, which is the most accurate statement?

Hull-White can fit the initial discount curve through its time-dependent drift and fit the term structure of volatility through σ(t) and mean reversion. Model 3 only fits the curve, since its constant volatility cannot reproduce varying volatilities. Both remain normal models, so negative rates are still possible.

  1. AHull-White cannot match the initial discount curve because σ(t) uses up the degrees of freedom
  2. BHull-White can match both the initial term structure of rates via the drift and the term structure of volatility via σ(t) and the mean-reversion parameterCorrect
  3. CModel 3 can match the term structure of volatility exactly because it has a time-dependent drift
  4. DHull-White removes the possibility of negative rates because volatility declines

Explanation

In Hull-White the time-dependent drift fits the initial curve and σ(t) (with mean reversion) fits volatility. Model 3's drift fits the curve but constant σ cannot fit a volatility term structure. Both are normal models, so negative rates remain possible.

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