FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A desk calibrates a Vasicek model to market prices of bond options and finds the fitted volatility σ is 1.2% while historical short-rate changes imply 0.9%. Which statement about the calibration is most appropriate?
Calibrating to option prices produces risk-neutral, market-implied parameters, which commonly differ from historical estimates because of risk premia and market imperfections. The gap between 1.2% and 0.9% is therefore not a model failure and does not imply negative mean reversion.
- ACalibration to option prices yields risk-neutral parameters, so differences from historical estimates can reflect the market price of risk and implied volatility premiaCorrect
- BThe model is invalid because implied and historical volatility must be identical under any measure
- CHistorical volatility should always replace the implied value when pricing options
- DThe difference proves that the mean reversion rate k is negative
Explanation
Option-implied parameters are calibrated to market prices under the risk-neutral measure, and they need not equal historical estimates. Implied volatility can differ because of risk premia and supply-demand effects. Volatility itself is unaffected by the measure in pure theory, but the market is not exactly Vasicek, so differences are normal and do not imply negative k.
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