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

A desk calibrates a Vasicek model and then re-estimates it with a higher σ, leaving k, the risk-neutral long-run mean rate and the current short rate unchanged. What is the effect on the model's long-maturity zero-coupon yields?

Long-maturity yields fall. In Vasicek, volatility does not change the expected rate path under the risk-neutral measure, but it increases the convexity benefit in bond prices. Higher zero prices mean lower yields, and the effect is largest at long maturities, approaching σ²/(2k²) at the limit.

  1. AThey rise, because greater volatility raises expected future rates
  2. BThey fall, because the convexity effect of higher volatility raises bond pricesCorrect
  3. CThey are unchanged, because volatility does not enter the risk-neutral drift
  4. DThey fall only for short maturities, because mean reversion removes the effect at long maturities

Explanation

In Vasicek the expected rate path depends on k and θ*, not σ. Higher σ increases the convexity term, which is roughly σ²/(2k²) at long maturities, and raises zero prices. Higher prices mean lower yields, with the effect larger at long maturities. Mean reversion limits the effect to a finite amount but does not remove it.

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