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

In the Vasicek model, which feature of the short-rate distribution at a future date is correct?

Vasicek short rates are normally distributed at any future date, so there is a positive probability of negative rates. Volatility is constant and shocks are additive, which produces a normal distribution rather than a lognormal one bounded at zero.

  1. ARates are lognormal, so they can never be negative
  2. BRates are normally distributed, so negative rates have positive probabilityCorrect
  3. CRates are chi-square distributed with a floor at zero
  4. DRates are normal only if k equals zero

Explanation

Vasicek has constant volatility and additive normal shocks, giving a normally distributed short rate at any future date. Hence negative rates occur with positive probability. Lognormal rates belong to models such as Black-Karasinski or Ho-Lee variants with proportional volatility.

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