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.

The correct answer is C. In the Cox-Ingersoll-Ross (CIR) model, the basis-point volatility of the short-term interest rate is presumed to be proportional to the square root of the rate. This characteristic is what differentiates the CIR model from simpler models where volatility is assumed to be independent of the short-term rate. The annualized basis-point volatility is represented as \( \sigma \times \sqrt{r} \), where \( \sigma \) is the volatility parameter and \( r \) is the short-term rate. Importantly, the CIR model ensures that the short-term rate cannot be negative because the basis-point volatility approaches zero as the short-term rate approaches zero, and the drift is positive when the short-term rate is zero. This feature is crucial for modeling interest rates, which are bounded below by zero but can theoretically extend upwards without bound. The other options provided are incorrect for the following reasons: A is incorrect because, in the Ho-Lee model, the drift of the interest rate process is time-varying, not constant. B is incorrect because the Ho-Lee model does not define a long-run equilibrium value for the short-term rate. D is incorrect because, in the CIR model, the volatility of the short-term rate is not assumed to decline exponentially to a constant long-run level; instead, it is proportional to the square root of the short-rate, as correctly stated in option C.

Author: LeetQuiz Editorial Team