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

A risk analyst at a bank uses the Ho-Lee model, dr = λ(t)dt + σ dw, to price interest rate derivatives. Which statement best describes the role of the time-dependent drift λ(t) in this model?

The time-dependent drift λ(t) in the Ho-Lee model is calibrated so model bond prices match the observed initial term structure. It is not a mean-reversion speed, does not shape volatility, and does not prevent negative rates, since rates are normally distributed.

  1. AIt is calibrated so the model's theoretical prices match the observed initial term structure of bond pricesCorrect
  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 maturity
  4. DIt ensures the short rate cannot become negative

Explanation

In Ho-Lee, λ(t) is chosen as a function of time so that the model reproduces the current market term structure (a no-arbitrage fit). There is no mean reversion in Ho-Lee, volatility is constant, and rates are normally distributed so they can be negative.

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