FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A trading desk wants a model that reproduces today's observed market zero-coupon bond prices exactly at every maturity. A quant proposes a Vasicek model with constant k, θ and σ. Which statement is correct?
Constant-parameter Vasicek cannot match an arbitrary market curve exactly because it has only a few parameters. Fitting the whole initial term structure requires a time-dependent drift, as in Ho-Lee or Hull-White, so a plain Vasicek model gives only an approximate fit.
- AWith constant parameters, the Vasicek curve has too few degrees of freedom to fit an arbitrary market curve exactly; a time-dependent θ(t) would be neededCorrect
- BConstant-parameter Vasicek fits any market curve exactly because the bond price formula is affine in r
- CVasicek fits the curve exactly once the short rate r0 is set equal to the longest-maturity market yield
- DVasicek fits the curve exactly if σ is calibrated separately for each maturity
Explanation
Vasicek with constant parameters has only a handful of inputs (r0, k, θ, σ), so it can fit only a limited family of curve shapes. Models like Ho-Lee and Hull-White use a time-dependent drift to match the initial curve. An affine price formula does not guarantee a fit. Setting r0 to the long yield or varying σ by maturity is not a valid calibration of this model.
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