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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

In the Vasicek model dr = a(μ − r)dt + σ dW, which statement about the short rate r is correct?

In the Vasicek model the short rate is normally distributed because the noise is additive and the drift is linear, so negative rates occur with positive probability. Non-negativity belongs to square-root models like CIR, not Vasicek.

  1. AThe short rate cannot become negative because the volatility is proportional to r
  2. BThe short rate is normally distributed and can become negative with positive probabilityCorrect
  3. CThe short rate is lognormally distributed at every future time
  4. DThe short rate drifts away from μ when a > 0
  5. The short rate has constant variance only if a = 0 and σ = 0

Explanation

Vasicek has additive Gaussian noise and mean reversion, so r(t) is normally distributed. A normal variable takes negative values with positive probability. The option claiming volatility proportional to r describes CIR-type behaviour, not Vasicek.

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