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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution

A risk analyst calibrates the Ho-Lee model, dr = λ(t)dt + σ dw, to a term structure of interest rates. Which statement best describes the role of the time-dependent drift λ(t) in this model?

The time-dependent drift in the Ho-Lee model is calibrated so that model bond prices match the observed market term structure. It does not provide mean reversion, change the constant volatility, or rule out negative rates, since rates are normally distributed.

  1. AIt is chosen so that model prices of the bonds match the observed market term structureCorrect
  2. BIt controls the speed at which the short rate reverts to a long-run mean
  3. CIt makes the volatility of the short rate decline exponentially with time
  4. DIt prevents the short rate from ever becoming negative

Explanation

In Ho-Lee, λ(t) is fitted to the initial term structure so that the model reproduces market bond prices. Mean reversion is absent in Ho-Lee (it appears in Vasicek), volatility is constant, and rates are normally distributed so negative rates are possible.

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