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 = 1.00% per year, a trader considers the distribution of the short rate 4 years ahead. Ignoring the drift, what is the standard deviation of the change in the short rate over 4 years?
The standard deviation of the short-rate change over four years is 2.00%. In the Ho-Lee model, variance grows linearly with time, so the standard deviation is the volatility of 1.00% multiplied by the square root of four, which equals 2.00%.
- A2.00%Correct
- B4.00%
- C1.00%
- D0.25%
Explanation
Rate changes are normal with variance σ²t, so the standard deviation is σ√t = 1.00% × √4 = 2.00%. Using σt gives 4.00%, which wrongly scales linearly with time.
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