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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution

A desk calibrates a CIR model and a Vasicek model to the same current yield curve. Compared with Vasicek, which feature of the CIR model is most relevant for pricing options when rates are very low?

CIR volatility falls as rates approach zero, which limits the chance of negative rates and gives a skewed, non-central chi-squared distribution for future rates. Vasicek has constant volatility and a normal distribution, so it allows negative rates. CIR keeps mean reversion.

  1. AVolatility declines as rates approach zero, which reduces the probability of negative rates and produces a skewed rate distributionCorrect
  2. BVolatility is unaffected by the level of rates, producing a symmetric normal distribution of future rates
  3. CRates are lognormal so that volatility in basis points is proportional to the rate level
  4. DMean reversion is removed, so rates follow a random walk with drift

Explanation

CIR's √r volatility shrinks near zero, pushing the distribution of future rates to be non-central chi-squared and right-skewed, with no negative rates under the Feller condition. Vasicek gives a normal distribution with constant volatility and positive probability of negative rates. CIR retains mean reversion and its volatility is not proportional to r.

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