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

A risk analyst reviews the Ho-Lee model, in which the short rate follows dr = λ(t)dt + σdw. Which statement best describes the role of the time-dependent drift λ(t) in this model?

The time-dependent drift λ(t) in Ho-Lee is calibrated so model prices match the observed market term structure. It is not a mean-reversion term and does not control volatility, which is constant. Normally distributed rates also mean negative rates remain possible.

  1. AIt is calibrated so that model prices of the chosen benchmark securities match their market prices, fitting the initial term structureCorrect
  2. BIt produces mean reversion of the short rate toward a long-run level at a constant speed
  3. CIt makes the short-rate volatility decline exponentially as maturity increases
  4. DIt guarantees that the short rate can never become negative

Explanation

In Ho-Lee, λ(t) is chosen as a function of time so the model reproduces the observed market curve (e.g., the prices of zero-coupon bonds). It does not create mean reversion (that is Vasicek) and does not affect volatility, which is a constant σ. Ho-Lee with normal rates allows negative rates.

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