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徐威廉 · 2024年10月28日

CIR模型的short rate为什么不能为负?

NO.PZ2023100703000098

问题如下:

A CRO of a hedge fund is asking the risk team to develop a term-structure model that is appropriate for fitting interest rates for use in the fund’s options pricing practice. The risk team is evaluating several interest rate models with time-dependent drift and time-dependent volatility functions. Which of the following is a correct description of the specified model?

选项:

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.

解释:

C is correct. In the 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 equals σ*sqart(r). Short-term rate in the CIR model cannot be negative because of the combined property that (i) basis-point volatility equals zero when short -term rate is zero, and (ii) the drift is positive when the short-term rate is zero. A is incorrect. In the Ho-Lee model, the drift of the interest rate process is presumed to be time-varying. B is incorrect. No long-run equilibrium value is defined in the Ho-Lee model. D is incorrect. The volatility of the short-term rate is assumed to be proportional to the square root of the short-rate in the CIR model.

CIR模型的short rate为什么不能为负?

1 个答案
已采纳答案

李坏_品职助教 · 2024年10月28日

嗨,从没放弃的小努力你好:


CIR model:

当利率r很低的时候,后面的σ*根号r dw这一项接近于0,也就是此时利率水平几乎不会波动了(很难继续降低到负数)。

此外,利率r为0的时候,前面的k*(θ-r)始终大于0,也保证了利率不会是负数。


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