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

A manager must choose between a normal model with constant basis-point volatility and a CIR model for hedging a book when the short rate has historically moved from 8% to 1%. Empirically, basis-point volatility fell as rates fell. Which conclusion is best supported?

CIR fits the observation that basis-point volatility falls when rates fall, because its volatility is sigma times the square root of the rate. A normal model holds volatility constant and so would overstate volatility at low rates. The two models do not imply the same volatility.

  1. ACIR better captures the observed link between rate level and volatility, while the normal model would overstate volatility at low ratesCorrect
  2. BThe normal model is preferable because it makes volatility fall as rates fall
  3. CBoth models imply the same volatility at every rate level, so the choice is irrelevant
  4. DCIR would overstate volatility at low rates because volatility is proportional to the rate squared

Explanation

CIR volatility σ√r declines as r falls, matching the observed pattern. A normal model holds basis-point volatility constant, so at 1% it would overstate volatility relative to the data. CIR volatility is not proportional to r squared, and the models differ in their volatility dependence.

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