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FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

A risk analyst compares the Vasicek model with the Cox-Ingersoll-Ross (CIR) model, where dr = k(θ - r)dt + σ√r dw. Which statement best describes how CIR differs from Vasicek in its treatment of volatility?

CIR makes volatility proportional to the square root of the short rate, so basis-point volatility increases as rates rise and shrinks near zero. With suitable parameters (the Feller condition) rates stay nonnegative, unlike Vasicek, which has constant volatility and allows negative rates.

  1. ABasis-point volatility is constant across all rate levels, so rates can become negative with equal probability at any level
  2. BBasis-point volatility rises with the level of the short rate, and with suitable parameters rates are kept from going negativeCorrect
  3. CBasis-point volatility falls as the short rate rises, which makes the model unable to produce mean reversion
  4. DVolatility is a deterministic function of time only, so it is independent of the level of the short rate

Explanation

In CIR the diffusion term is σ√r, so basis-point volatility increases with the rate level and shrinks as the rate approaches zero. When the Feller condition 2kθ ≥ σ² holds, the rate cannot reach zero. Vasicek has constant basis-point volatility and permits negative rates.

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