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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-term rate is assumed to be proportional to the square root of the rate, and short-term rates cannot be negative. This is because the basis-point volatility is defined as \( \sigma \times \sqrt{r} \), where \( \sigma \) is the constant of proportionality and \( r \) is the short-term rate. This relationship ensures that volatility is zero when the short-term rate is zero, which prevents negative rates. The CIR model is particularly useful for modeling interest rates because it allows for mean reversion and ensures that interest rates remain positive, which is a realistic assumption for financial markets.
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The Chief Risk Officer (CRO) of a hedge fund has tasked the risk department with developing a term-structure model that can effectively adjust interest rates for the fund's options pricing strategy. The risk department is evaluating different interest rate models, specifically those that feature both time-varying drift and time-varying volatility. Which model accurately represents 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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