FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution
In the Ho-Lee model, the short rate follows dr = λ(t)dt + σ dw with σ = 1.20% per year. A risk manager wants the standard deviation of the short rate change over one month (1/12 year). Which is the closest value?
The standard deviation scales with the square root of time: 1.20% times the square root of one twelfth is about 0.346%. Dividing by twelve instead (0.10%) wrongly scales volatility linearly with time, while 1.20% ignores the one-month horizon.
- A0.035%
- B0.100%
- C0.346%Correct
- D1.200%
Explanation
Standard deviation over dt is σ√dt = 1.20% × √(1/12) = 1.20% × 0.2887 = 0.3464%. Using 1.20%/12 = 0.10% scales linearly with time, which is the wrong treatment since variance scales with time.
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