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

A risk analyst uses a model in which the short rate follows dr = λ dt + σ dw under the risk-neutral measure, with λ = 0.20% per year, σ = 1.00% per year and a current short rate of 3.00%. What is the expected short rate in 2 years under this risk-neutral process?

The expected short rate in two years is 3.40%. With a constant risk-neutral drift, the expected rate equals the starting rate plus drift times time: 3.00% plus 0.20% for each of two years. Volatility does not change the expected value.

  1. A3.20%
  2. B3.40%Correct
  3. C3.80%
  4. D3.00%

Explanation

With constant drift the expected rate is r0 + λt = 3.00% + 0.20% × 2 = 3.40%. The 3.20% option counts only one year of drift. The 3.00% option is the zero-drift model, which ignores λ.

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