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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

A Vasicek model has k = 0.40 per year. Approximately how long is the half-life of a deviation of the short rate from θ, and what does the half-life imply?

The half-life is about 1.73 years, from ln(2)/k = 0.6931/0.40. It means half of any current deviation of the short rate from θ is expected to have disappeared by then; the rate does not fully reach θ in that time.

  1. AAbout 1.73 years; half of any deviation is expected to disappear by thenCorrect
  2. BAbout 2.50 years; the full deviation is expected to disappear by then
  3. CAbout 0.80 years; the volatility halves by then
  4. DAbout 1.73 years; the rate is expected to reach θ by then

Explanation

The deviation decays as e^(−kt). Setting e^(−kt) = 0.5 gives t = ln2/k = 0.6931/0.40 = 1.73 years. At that time half the gap is expected to remain closed, not all of it. Option D wrongly says the rate reaches θ; 2.5 is simply 1/k.

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