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Answer: In the CIR model, yield volatility is specified as being constant while basis-point volatility is allowed to vary.
## Explanation In the Cox-Ingersoll-Ross (CIR) model: - **Yield volatility is constant** - This is a key feature of the CIR model where the volatility of yields is specified as constant - **Basis-point volatility varies** - The basis-point volatility (absolute volatility) is proportional to the square root of the interest rate level This means that: - When interest rates are high, basis-point volatility is high - When interest rates are low, basis-point volatility is low - The model prevents negative interest rates due to the square root specification **Analysis of other options:** - **A**: Incorrect - Low interest rates lead to low basis-point volatility, and the CIR model prevents negative rates - **B**: Incorrect - Basis-point volatility depends on the interest rate level, not the mean reversion factor - **D**: Incorrect - Yield volatility and basis-point volatility are distinct concepts in the CIR model The CIR model's specification ensures that volatility decreases as rates approach zero, which prevents negative interest rates while maintaining constant yield volatility.
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An analyst is studying term structure models that incorporate measures of volatility into the interest rate process. The analyst focuses on the Cox-Ingersoll-Ross (CIR) model and its treatment of volatility of the short-term interest rate. Which of the following statements is correct regarding the yield volatility and basis-point volatility in the CIR model?
A
Periods of extremely low short-term interest rates are accompanied by high basis-point volatility, which increases the possibility of negative interest rates in the CIR model.
B
In the CIR model, basis-point volatility is specified as a decreasing function of the mean reversion factor.
C
In the CIR model, yield volatility is specified as being constant while basis-point volatility is allowed to vary.
D
Basis-point volatility and yield volatility are used interchangeably to measure the same volatility in the CIR model.
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