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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 λ(t) implied by calibration to the initial curve equals the slope of the forward-rate curve plus a term involving σ. Which expression is correct?

The calibrated drift is the slope of the forward-rate curve plus σ² times t. The σ²t term is the convexity adjustment needed so that model bond prices match the initial curve. Other forms have the wrong sign or lack the time factor.

  1. Aλ(t) = ∂F(0,t)/∂t − σ²t
  2. Bλ(t) = ∂F(0,t)/∂t + σ²tCorrect
  3. Cλ(t) = F(0,t) + σ²t
  4. Dλ(t) = ∂F(0,t)/∂t + σ²/2

Explanation

Fitting the initial curve in Ho-Lee gives λ(t) = ∂F(0,t)/∂t + σ²t. The σ²t term is the convexity adjustment that offsets the Jensen's inequality effect in bond prices. Subtracting it or omitting the time factor is incorrect.

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