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

A desk calibrates a Ho-Lee model to an upward-sloping forward curve and then notes that simulated short rates in the model sometimes become negative. Which is the most appropriate conclusion?

Negative simulated rates are an inherent feature of Ho-Lee because the short rate is normally distributed and has no mean reversion or floor. Fitting the curve does not change this, drift sign is not the cause, and raising volatility makes negative rates more likely.

  1. AThe calibration is flawed, because a model fitted to market prices cannot produce negative rates
  2. BThis is a known feature of Ho-Lee, since rates are normally distributed with no mean reversionCorrect
  3. CNegative rates occur only if the drift λ(t) is negative
  4. DAdding a larger σ will eliminate negative rates

Explanation

Ho-Lee rates are normally distributed at each date, so there is always positive probability of negative values, regardless of drift sign. Perfect curve fit does not remove this. Raising σ increases the chance of negative rates.

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