Answer: In the Cox-Ingersoll-Ross model, the basis-point volatility of the short-term rate is presumed to be proportional to the square root of the rate.

## Explanation **C is correct.** In the Cox-Ingersoll-Ross (CIR) model, the basis-point volatility of the short-term rate is indeed proportional to the square root of the rate. This is a key characteristic of the CIR model that distinguishes it from other term structure models. **Key Features of CIR Model:** - **Volatility Structure**: The annualized basis-point volatility equals σ × √r, where σ is a constant volatility parameter and r is the short-term interest rate - **Non-Negative Rates**: The model ensures that interest rates cannot become negative due to two properties: 1. Basis-point volatility equals zero when the short-term rate is zero 2. The drift is positive when the short-term rate is zero - **Mean Reversion**: The model incorporates mean reversion, where rates tend to move toward a long-run equilibrium level **Why Other Options Are Incorrect:** - **A is incorrect**: In the Ho-Lee model, the drift is time-dependent, not constant. The model allows for a time-varying drift parameter to fit the initial term structure. - **B is incorrect**: The Ho-Lee model does not define a long-run equilibrium value for interest rates. It's a no-arbitrage model that focuses on fitting the current term structure rather than incorporating mean reversion. - **D is incorrect**: The CIR model does not assume that volatility declines exponentially to a constant long-run level. Instead, it assumes volatility is proportional to the square root of the interest rate level. **Model Comparison:** - **Ho-Lee Model**: Time-dependent drift, constant volatility, no mean reversion - **CIR Model**: Mean-reverting drift, volatility proportional to √r, ensures non-negative rates This understanding is crucial for proper model selection in options pricing and risk management applications.

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