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

A risk manager notes that a Ho-Lee model calibrated to today's curve fits all current bond prices exactly, yet is criticized for its volatility structure. Which is the key limitation of the model related to volatility?

The main volatility limitation is that Ho-Lee uses one constant volatility for all horizons, so it cannot reproduce a term structure of volatility. Exponentially declining volatility comes from mean reversion, as in Vasicek, and the drift calibration does not determine volatility.

  1. AVolatility is constant across time, so it cannot capture a term structure of volatility in ratesCorrect
  2. BVolatility depends on the rate level, producing a lognormal distribution
  3. CVolatility declines exponentially due to mean reversion, understating long-term risk
  4. DVolatility is determined by the drift, so calibration fixes it automatically

Explanation

Ho-Lee has a single constant σ and no mean reversion, so it cannot generate a declining volatility term structure. Rate-dependent volatility belongs to models like CIR or Black-Karasinski; exponentially decaying volatility belongs to Vasicek. Drift calibration is separate from σ.

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