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Archie · 2023年04月27日

CIR model

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2020033001000073

问题如下：

Which of the following statements is an advantage of the CIR model?

选项：

A.

During periods of high inflation, basis-point volatility decreases.

B.

Interest rates are always non-negative.

C.

Out-of-the money option prices may differ with the use of normal or lognormal distributions.

D.

Long-run interest rates may not hover around a mean-reverting level.

解释：

B is correct.

考点：CIR model

解析：

A. Basis-point volatility increases during periods of high inflation.

C. It is a disadvantage of CIR model.

D. CIR model is a mean-reverting model.

老师您好

我有点不明白为什么它是非负的。前一半让他能够均值回归，后一半有个根号r，这是非负的，但是后一半里面也有个ε，这个东西在正负一这样变化，也能够让dr变成负的？我有点混乱，也可能理解有什么偏差，麻烦老师解答谢谢

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pzqa27 · 2023年04月28日

嗨，从没放弃的小努力你好：


后半段的确有可能出现负值，但是我们需要看整体的式子来判断正负，当R小于θ的时候，前半段的牵引项必然是正的，此时后半段哪怕真的取到负的值了，但是R的0.5次方是个比较小的数，几乎可以忽略不计了，因此总体是大于0的，而当R大于θ的时候，此时前半段牵引项会把R向下拉，如果只有牵引项，最多也就拉回θ的位置，θ虽然可以设置成负值，但是现实中θ为负几乎不可能，后半段同理哪怕ε取到负值，R的0.5次方也是个很小的书，因此后面的随机项一般不至于把利率拉到0以下

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努力的时光都是限量版，加油！

Archie · 2023年04月29日

绝了，茅塞顿开

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