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金融民工阿聪 · 2021年03月07日

这么多模型，是不是只有CIR是可以得出利率不会小于0的结果的

  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.

这7个模型中，是不是只有CIR是可以得出利率不会小于0的结果的

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品职答疑小助手雍 · 2021年03月08日

嗨，从没放弃的小努力你好：


CIR和lognormal都不会小于0。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

yuyukou · 2022年04月10日

老师，vasicek 会小于0么？

品职答疑小助手雍 · 2022年04月11日

不是单纯的均值复归的原因。

当短期利率降到0（或者接近0）的时候，根据CIR的公式你会发现：

均值复归项会是一个正值，而后面的波动项是要乘以根号r的，根号r等于0或者接近0，所以下一个阶段利率必定上升。

所以整个公式细分下来不会降到0以下。

品职答疑小助手雍 · 2022年04月10日

会

yuyukou · 2022年04月10日

老师请问，CIR和vasicek都是均值回归的模型，为什么CIR不会小于0，vasicek就会？那说明均值回归模型，不能保证利率大于0，是么

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