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C_M_ · 2024年09月05日

99%

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.

99% confidence level就是1000个里面有10个exception,跟实际的25个相比,说明实际的confidence level得是97.5%。那实际发生的有一部分本应该accept的被视为reject,也就是type I error变大,这样理解对不

1 个答案

pzqa27 · 2024年09月06日

嗨,从没放弃的小努力你好:


不对。

VaR的回测里有2个分位点,第一个是VaR本身的分位点,比如题目里给的是99%。第二个是回测的分位点,即假设检验的分位点。这个题目里没有给出来。

对于99%的VaR来说,1000天里只能有最多10天超过VaR.而真实的情况是有25天超过了VaR,由于10天和25天之间差距过大,我们拒绝假设检验的原假设,因此可能造成的风险是拒绝一个真假设,所以是type I error。

而对于“99% confidence level就是1000个里面有10个exception,跟实际的25个相比,说明实际的confidence level得是97.5%。那实际发生的有一部分本应该accept的被视为reject,也就是type I error变大”这个轮式中,把VaR分位点和回测的分位点混淆了起来,尽管结论一致,但是推导过程是不对的。

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