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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, and short-term rates cannot be negative.
The correct answer is C. In the Cox-Ingersoll-Ross (CIR) model, the basis-point volatility of the short rate is not independent of the short rate as other simpler models assume. The annualized basis-point volatility is given by \( g \times \sqrt{r} \), where \( g \) is a constant and \( r \) is the short-term rate. Importantly, the short-term rate in the CIR model cannot be negative due to two properties: (i) the basis-point volatility equals zero when the short-term rate is zero, and (ii) the drift is positive when the short-term rate is zero. This feature of the CIR model is what makes option C the correct description of the specified model for fitting interest rates with time-dependent drift and volatility functions.
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A Chief Risk Officer (CRO) of a hedge fund has tasked the risk department with developing a term-structure model to effectively adjust interest rates for the hedge fund's options pricing strategy. In pursuit of this objective, the risk department is evaluating different interest rate models characterized by their ability to accommodate both time-varying drift and time-varying volatility functions. Which model accurately encapsulates these characteristics?
A
In the Ho-Lee model, the drift of the interest rate process is presumed to be constant.
B
In the Ho-Lee model, when the short-term rate is above its long-run equilibrium value, the drift is presumed to be negative.
C
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, and short-term rates cannot be negative.
D
In the Cox-Ingersoll-Ross model, the volatility of the short-term rate is presumed to decline exponentially to a constant long-run level.
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