CIR

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 that incorporate either time-dependent drift or 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 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.

解释：

中文解析：

C是正确的。在CIR模型中，短期利率的基点波动率并不是想起他模型一样，独立于短期利率。年化的基点波动率等于𝜎*sqrt(r)。CIR模型中的短期利率不能是负值，因为(i)短期利率为0时，基点波动率等于零，(ii)当短期率为0时，漂移项是正的。

A是不正确的。在Ho-Lee模型中，利率的漂移是随时间变化。

B是不正确的。在Ho-Lee模型中没有定义长期均衡值。

D不正确。在CIR模型中，短期利率的波动率与短期利率的平方根成比例。

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*sqrt(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.