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

In a Ho-Lee model with constant volatility σ = 1.20% per year, the short rate is currently 4.00%. Ignoring the drift's effect on dispersion, what is the standard deviation of the short rate at a horizon of 4 years, and what is the distribution of the rate at that horizon?

The standard deviation is 1.20% times the square root of 4, which is 2.40%, and the rate is normally distributed. Variance grows linearly with time in Ho-Lee, so volatility scales with the square root of time, not linearly.

  1. A2.40%, normalCorrect
  2. B4.80%, normal
  3. C2.40%, lognormal
  4. D1.20%, normal

Explanation

Ho-Lee variance of r(T) is σ²T, so the standard deviation is σ√T = 1.20% × √4 = 2.40%. The rate is normally distributed because dr has a constant volatility and a deterministic drift. Using σT = 4.80% is the key mistake of scaling linearly in time.

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