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

A desk wants its Vasicek model to price a bond option consistently with market quotes. Which calibration practice is most appropriate for the volatility parameter σ?

The volatility parameter σ, along with the mean reversion speed, is best calibrated by fitting model prices to liquid option prices such as caps or bond options, since the bond curve alone contains little information about volatility. Arbitrary settings like zero volatility or σ equal to the short rate are unjustified.

  1. ASet σ to zero so that the option is priced at intrinsic value
  2. BChoose σ, with k, so that model prices of liquid options (e.g., caps or bond options) match market prices as closely as possibleCorrect
  3. CSet σ equal to the current short rate
  4. DSet σ so that the model price of every bond equals its face value

Explanation

Volatility parameters are typically implied from liquid option prices, since the bond curve alone says little about volatility. Setting σ to zero removes randomness, and tying σ to the rate level or to face value has no theoretical basis.

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