FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift
Under Model 1, dr = σ dw, with σ = 90 basis points per year. A trader wants the standard deviation of the short rate over a 4-year horizon. Which value is correct?
The standard deviation is 180 basis points. Under the zero-drift normal model, the short rate's variance grows proportionally with time, so the standard deviation equals volatility times the square root of the horizon: 90 times the square root of 4.
- A180 basis pointsCorrect
- B360 basis points
- C90 basis points
- D45 basis points
Explanation
Variance of r(T) is σ²T, so the standard deviation is σ√T = 90 × √4 = 180 bps. The 360 figure wrongly multiplies σ by T (a linear scaling), which ignores that variance grows linearly with time.
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