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Ella · 2024年11月02日

如何判断的1-99.996%处于拒绝域内啊,题目也没给置信水平呀

NO.PZ2023100703000036

问题如下:

Basel II requires a backtest of a bank’s internal value at risk (VaR) model (IMA). Assume the bank’s ten-day 99% VaR is $1 million (minimum of 99% is hard-wired per Basel). The null hypothesis is: the VaR model is accurate. Out of 1,000 observations, 25 exceptions are observed (we saw the actual loss exceed the VaR 25 out of 1000 observations).

选项:

A.We will probably call the VaR model good (accurate) but we risk a Type I error. B.We will probably call the VaR model good (accurate) but we risk a Type II error. C.We will probably call the model bad (inaccurate) but we risk a Type I error. D.We will probably call the model bad (inaccurate) but we risk a Type II error.

解释:

The probability of 25 or more exceptions will only be observed 1 – 99.996%. So, we reject the model. Null = good model. To decide the model is bad model is to reject null and this implies a risk of type I error.

如何判断的1-99.996%处于拒绝域内啊,题目也没给置信水平呀

1 个答案
已采纳答案

pzqa39 · 2024年11月03日

嗨,从没放弃的小努力你好:


题目提到的“十天99% VaR 是1百万”意味着银行在99%的情况下,损失不会超过 1百万。由此可知,1%的情况下会有异常,即实际损失超过VaR。在假设检验中,我们通常设定原假设为“模型准确”,这意味着在我们的例子中,实际异常发生的概率应该等于VaR所反映的1%。备择假设则是“模型不准确”,即实际异常发生的概率大于1%。题目提供了 1,000 次观测,报告了 25 次异常(即损失超过了 1百万)。


如果我们假设原假设成立,即实际的异常率是1%,在 1,000 次观测中,按 99% VaR 标准,异常观测值的期望次数应该为 1%×1000=10 次。实际观测到的异常次数为 25,比期望的 10 次显著高出很多。异常次数在原假设下的理论期望之外,并且 z-score 显著高于99%临界值,所以我们要拒绝原假设。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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