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wawjbng · 2021年06月07日

问一道题:NO.PZ2018122701000033 [ FRM II ]

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).  (Binomial CDF)

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:

C is correct.

考点 : Backtesting VaR

解析 :H0 : the VaR model is accurate. Hα: the VaR model is inaccurate.

Z=xpTp(1p)T=251%×10001%×(11%)×1000=4.77Z=\frac{x-pT}{\sqrt{p(1-p)T}}=\frac{25-1\%\times1000}{\sqrt{1\%\times(1-1\%)\times1000}}=4.77

As 4.77 is larger than 2.58, we reject the null hypothesis. Therefore, the model is bad model, and this implies a risk of type I error.

请问老师,为什么是一类错误不是二类错误呢

1 个答案

品职答疑小助手雍 · 2021年06月07日

嗨,爱思考的PZer你好:


因为原置信度是99%,所以在1000个样本中,应该只有1000*1%=10个例外。但题目中却说检验出了25个例外。所以原模型的置信度并不准,它是一个坏模型,我们拒绝它,但这毕竟冒了“去真”的风险,因此也就是冒着第一类错误的风险。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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NO.PZ2018122701000033 问题如下 Basel II requires a backtest of a bank’s internal value risk (VaR) mol (IMA). Assume the bank’s ten-y 99% Vis $1 million (minimum of 99% is harwireper Basel). The null hypothesis is: the Vmol is accurate. Out of 1,000 observations, 25 exceptions are observed (we sthe actuloss exceethe V25 out of 1000 observations).  (BinomiC) We will probably call the Vmol good (accurate) but we risk a Type I error. We will probably call the Vmol good (accurate) but we risk a Type II error. We will probably call the mol bad (inaccurate) but we risk a Type I error. We will probably call the mol bad (inaccurate) but we risk a Type II error. C is correct. 考点 Backtesting V解析 H0 : the Vmol is accurate. Hα: the Vmol is inaccurate.Z=x−pTp(1−p)T=25−1%×10001%×(1−1%)×1000=4.77Z=\frac{x-pT}{\sqrt{p(1-p)T}}=\frac{25-1\%\times1000}{\sqrt{1\%\times(1-1\%)\times1000}}=4.77Z=p(1−p)T​x−pT​=1%×(1−1%)×1000​25−1%×1000​=4.774.77 is larger th2.58, we rejethe null hypothesis. Therefore, the mol is bmol, anthis implies a risk of type I error. 我可以计算出Z= (x-pxT)/sqt[px(1-p)xT] = (25-1%x1000)/sqt[1x(1-1%)x1000] = 4.77 大于2.58,所以拒绝原假设,因此这是一个bmol。但是从哪判断这是Type I 还是type II risk? 看了之前的,还是不知道什么意思。

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