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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

Under Model 1 with zero drift and σ = 100 bp per year, the current short rate is 3.00%. Using a monthly-step tree with normal shocks, what is the standard deviation of the short rate three years ahead, ignoring convexity effects on the mean?

The standard deviation of the short rate after three years is σ√T = 100 × √3 ≈ 173.2 basis points. Variance grows linearly with time, so standard deviation grows with the square root of time, not linearly.

  1. A100 bp
  2. B300 bp
  3. C173.2 bpCorrect
  4. D57.7 bp

Explanation

Variance accumulates linearly with time: standard deviation at T = σ√T = 100 × √3 = 173.2 bp. Using 300 bp scales linearly with time, which is a mistake. Using 100/√3 divides rather than multiplies.

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