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

In a Ho-Lee model with constant volatility σ = 1.00% per year, the short rate is 4.00% today and the drift λ(t) = 0.30% per year for all t. Ignoring any convexity effect on the expectation of the rate itself, what is the expected short rate after 2 years?

The expected short rate is 4.60%. In Ho-Lee the expected rate equals the initial rate plus drift times time, so 4.00% plus 0.30% for each of two years gives 4.60%. Volatility does not change the expected rate itself.

  1. A4.30%
  2. B4.60%Correct
  3. C5.00%
  4. D4.00%

Explanation

Since dr = λ dt + σ dw, E[r(T)] = r0 + λT = 4.00% + 0.30% × 2 = 4.60%. 4.30% uses one year only. 5.00% wrongly adds σ×T.

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