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

A one-factor normal model with constant volatility has a short rate of 5% and annual volatility σ of 100 bps. Ignoring drift, which is the approximate one-month (1/12 year) standard deviation of the rate change?

The one-month standard deviation is about 0.289%, found as 1.00% times the square root of one-twelfth. Volatility scales with the square root of time, not linearly, so using 1/12 directly would understate it at 0.083%.

  1. A0.289%Correct
  2. B1.00%
  3. C0.083%
  4. D0.120%

Explanation

Standard deviation over time dt equals σ√dt. 1.00% × √(1/12) = 1.00% × 0.2887 = 0.289%. Multiplying by 1/12 instead of its square root gives 0.083%, which is the key error.

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