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

A risk manager observes that historically the basis-point volatility of short rates has fallen when the level of rates is very low, and wants a model reflecting that volatility depends on the rate level but still avoids the unrealistic implication of a constant proportional volatility. Which model class best fits this feature?

A square-root volatility model such as Cox-Ingersoll-Ross fits best, because basis-point volatility increases with the rate level but less than proportionally, and rates remain non-negative. Constant-volatility normal models such as Ho-Lee ignore level dependence entirely.

  1. AHo-Lee model with constant normal volatility
  2. BA model with volatility proportional to the square root of the rate, such as the Cox-Ingersoll-Ross modelCorrect
  3. CA model with deterministic drift and zero volatility
  4. DA model with volatility independent of the rate level and time

Explanation

The CIR model sets volatility proportional to √r, so basis-point volatility rises with the rate but less than proportionally, and rates stay non-negative. Constant-volatility models ignore the level dependence.

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