FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift
Under Model 1 (dr = σ dw), the current short rate is 4.00% and annualized basis-point volatility σ is 100 bps. What is the standard deviation of the short rate at a 4-year horizon?
The standard deviation is 2.00%. In the zero-drift normal model the standard deviation of the short rate grows with the square root of time, so 100 bps times the square root of 4 gives 200 bps.
- A1.00%
- B2.00%Correct
- C4.00%
- D0.50%
Explanation
Variance of r_T is σ²T, so the standard deviation is σ√T = 100 bps × √4 = 200 bps = 2.00%. Using 100 bps × 4 = 400 bps (4.00%) wrongly scales linearly with time, and 1.00% ignores the horizon.
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