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Archie · 2023年04月27日

CIR model

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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