Skip to content

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

In the Vasicek model dr = k(θ − r)dt + σdw, an analyst calibrates the parameters to the current term structure of interest rates by choosing k, θ, and σ to minimize pricing errors across a set of bond prices. Which statement best describes a key limitation of this calibration approach?

Because the Vasicek model has only a few constant parameters, it generally cannot reproduce an arbitrary observed term structure exactly. This limitation motivates extensions with time-dependent drift, such as Hull-White, which fit the initial curve by construction.

  1. AWith constant parameters, the model generally cannot fit an arbitrary observed term structure exactlyCorrect
  2. BThe model cannot be calibrated because it has no closed-form bond price
  3. CCalibration requires that the short rate be deterministic
  4. DThe calibration fixes σ equal to the long-run mean θ

Explanation

Vasicek has only three constant parameters, so it can match only a limited set of curve shapes. A market curve with arbitrary shape generally cannot be fitted exactly, which motivates time-dependent θ(t) extensions such as Hull-White. The model does have closed-form bond prices, so the other options are wrong.

Did you get it right without looking?

One question tells you little. A timed set on The Vasicek and Gauss+ Models shows your real accuracy, how long you take and where you lose marks.

Practise The Vasicek and Gauss+ ModelsFree diagnostic mock

More The Vasicek and Gauss+ Models questions