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FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

When calibrating a Vasicek model to market data, a practitioner finds that the model cannot exactly match today's observed yield curve using constant θ, k and σ. Which modification is the standard remedy in the term structure model literature?

The usual remedy is to make the drift time-dependent so the model fits today's yield curve exactly, as in Ho-Lee or Hull-White extensions. Constant parameters in Vasicek give too few degrees of freedom to match an arbitrary observed term structure.

  1. AAllow the drift to be time-dependent (a deterministic function of time) so the model fits the initial curve exactly, as in the Ho-Lee or Hull-White extensionsCorrect
  2. BRemove mean reversion entirely and set k to infinity
  3. CReplace the normal shocks with lognormal shocks, which guarantees a perfect fit
  4. DFit only the highest-maturity yield and ignore the others

Explanation

Constant-parameter Vasicek has too few degrees of freedom to fit an arbitrary curve. Making the drift a function of time lets the model match the initial term structure exactly, as in Hull-White. Setting k to infinity freezes the rate, lognormal shocks do not guarantee a fit, and ignoring maturities defeats calibration.

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