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

In a lognormal short-rate model, dr = a·r·dt + σ·r·dw, with a = 3% and σ = 20%, what is the drift of ln(r) per year, after applying Ito's lemma?

By Ito's lemma the drift of ln(r) is a minus half of σ squared. This gives 3% − (0.20² / 2) = 3% − 2% = 1% per year. Using 3% ignores the convexity correction, and adding the correction instead would wrongly give 5%.

  1. A1%Correct
  2. B3%
  3. C5%
  4. D−1%

Explanation

By Ito's lemma, d ln r = (a − σ²/2)dt + σ dw. Here σ²/2 = 0.04/2 = 0.02, so the drift is 0.03 − 0.02 = 0.01, or 1%. Using 3% ignores the Ito correction, and 5% adds the correction instead of subtracting it.

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