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

In the Ho-Lee model with constant σ, the drift is calibrated to the forward curve. Let F(t) be the instantaneous forward rate. The drift is λ(t) = ∂F(t)/∂t + σ²t. At t = 5, the forward curve has slope 0.20% per year and σ = 1.00% per year (0.01). What is λ(5)?

λ(5) is 0.25% per year. The drift equals the forward-rate slope plus the convexity term σ²t. With σ = 1% the convexity term is 0.0001 × 5 = 0.05%, so 0.20% + 0.05% = 0.25%. Ignoring convexity would give 0.20%.

  1. A0.25% per yearCorrect
  2. B0.20% per year
  3. C0.70% per year
  4. D0.45% per year

Explanation

σ²t = 0.0001 × 5 = 0.0005 = 0.05%. Adding the forward slope gives 0.20% + 0.05% = 0.25% per year. The 0.20% answer omits the convexity term, 0.70% uses σ·t, and 0.45% subtracts nothing but misapplies the term.

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