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

A bank's treasury is choosing between a normal (Vasicek-type) model and a CIR model for valuing options in a period of very low interest rates near 0.25%. Which is the most valid reason to prefer CIR?

CIR is attractive at very low rates because its volatility shrinks as the rate approaches zero, and when the Feller condition holds the short rate cannot become negative. A constant-volatility normal model can produce negative rates, which may be undesirable in that setting.

  1. ACIR produces a deterministic short rate path, which simplifies hedging
  2. BCIR allows negative rates with equal likelihood to positive rates
  3. CCIR volatility declines as rates approach zero and, under the Feller condition, rates stay nonnegativeCorrect
  4. DCIR has constant basis-point volatility, matching observed behavior at low rates

Explanation

CIR's sqrt(r) volatility shrinks near zero and mean reversion pulls rates up, so rates remain nonnegative (strictly positive if the Feller condition holds). Vasicek-type models with constant volatility can yield negative rates.

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