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Answer: In the Cox-Ingersoll-Ross model, the basis-point volatility of the short-term rate is assumed to be proportional to the square root of the rate, and short-term rates cannot be negative.
The correct answer is C. The Cox-Ingersoll-Ross (CIR) model is characterized by a basis-point volatility of the short-term interest rate that is proportional to the square root of the rate. This implies that as the short-term rate approaches zero, the volatility also approaches zero, preventing negative rates. This feature is unique to the CIR model and distinguishes it from other term structure models. The CIR model also assumes that the drift is positive when the short-term rate is zero, which further supports the non-negativity of the short-term rate. The other options provided are incorrect for the following reasons: A. The Ho-Lee model assumes a time-varying drift, not a constant one. B. The Ho-Lee model does not define a long-run equilibrium value for the short-term rate. D. The volatility of the short-term rate in the CIR model is not assumed to decline exponentially to a constant long-run level; instead, it is proportional to the square root of the short-rate. The explanation provided in the file content gives a clear understanding of why option C is the correct choice and why the other options are incorrect, based on the specific characteristics of the Ho-Lee and CIR models.
Author: LeetQuiz Editorial Team
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As part of enhancing the fund’s options pricing strategy, the Chief Risk Officer (CRO) of a hedge fund has instructed the risk team to develop a term-structure model that can accurately adjust interest rates. The risk team is evaluating different interest rate models, specifically those that incorporate either time-dependent drift or time-dependent volatility functions. Identify which of the following options correctly represents the type of model being described.
A
In the Ho-Lee model, the drift of the interest rate process is assumed to be constant.
B
In the Ho-Lee model, when the short-term rate is above its long-run equilibrium value, the drift is assumed to be negative.
C
In the Cox-Ingersoll-Ross model, the basis-point volatility of the short-term rate is assumed to be proportional to the square root of the rate, and short-term rates cannot be negative.
D
In the Cox-Ingersoll-Ross model, the volatility of the short-term rate is assumed to decline exponentially to a constant long-run level.
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