FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A trading desk calibrates a Vasicek model with constant k, θ and σ to a small set of swap-implied rates and finds it cannot reproduce today's observed zero-coupon curve exactly, which is needed to price bond options consistently with market bond prices. Which modification best addresses this problem?
Make the long-run mean time-dependent, θ(t), and fit it to the observed curve. Constant-parameter Vasicek has too few parameters to match an arbitrary term structure, whereas a time-varying drift target matches today's curve exactly and keeps mean reversion and tractable bond-option pricing.
- AMake the long-run mean a deterministic function of time, θ(t), chosen to fit the observed curveCorrect
- BIncrease the mean-reversion speed k until the model curve matches the market curve
- CSet σ to zero so the model curve equals the forward curve
- DReplace the normal rate distribution with a constant rate
Explanation
Constant-parameter Vasicek has too few degrees of freedom to fit an arbitrary curve. Allowing the drift target θ(t) to vary with time (the Hull-White extension) lets the model match the initial curve exactly while retaining mean reversion and the tractable option formulas. Changing k alone gives only a limited family of shapes, and setting σ to zero removes the randomness needed to price options.
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