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

In Tuckman's 'Art of Term Structure Models' framework, Model 3 specifies the short-rate process as dr = λ(t)dt + σ dw with constant volatility σ. The Hull-White model extends this by allowing which feature?

The Hull-White model allows time-dependent volatility σ(t) together with mean reversion in the drift. This lets it be fitted to the market term structure of volatility, whereas Model 3 has only a time-dependent drift and a constant volatility with no mean reversion.

  1. AThe drift to depend on the short rate through mean reversion, with volatility held at zero
  2. BA time-dependent volatility σ(t) that can be fitted to the term structure of volatility, plus mean reversion in the driftCorrect
  3. CLognormal rather than normal short-rate changes, with a constant volatility
  4. DA volatility that depends on the level of the short rate through a square-root term

Explanation

Model 3 has a time-dependent drift but constant volatility and no mean reversion. The Hull-White (extended Vasicek) model adds mean reversion with a time-dependent drift and a time-dependent volatility σ(t), allowing calibration to market volatilities. Lognormal and square-root dynamics belong to other models (Black-Karasinski, CIR).

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