Skip to content

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

In Tuckman's treatment of term structure models, Model 3 is dr = λ(t)dt + σ dw, where the drift is time-dependent and the volatility is constant. A risk manager wants a model that allows the volatility of the short rate to differ across maturities of the calibrated volatility curve, such as a declining volatility term structure. Which model best fits this need?

The Hull-White model with time-dependent volatility σ(t) is the right choice. It lets the short-rate volatility change over time to match a volatility term structure, whereas Ho-Lee, Model 1 and Vasicek all use a constant volatility parameter and cannot fit a declining curve.

  1. AHo-Lee model with a constant σ
  2. BModel 1 with a constant drift
  3. CVasicek model with a constant long-run mean
  4. DHull-White model with a time-dependent σ(t)Correct

Explanation

The Hull-White (extended Vasicek) model in Tuckman's form is dr = k[θ(t) − r]dt + σ(t)dw, so volatility can vary with time and be fitted to a volatility curve. Ho-Lee and Model 1 have constant σ, and Vasicek has constant parameters, so none can match a declining volatility term structure.

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