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小猫批脸 · 2023年01月13日

这里的1000个观察值是代表着1000个交易日里的数据吗?

NO.PZ2018122701000033

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.

如题

1 个答案

李坏_品职助教 · 2023年01月13日

嗨,努力学习的PZer你好:


题目说的是10天的VaR,所以1000个观测值的意思是:有1000个10天的收益数据,在这1000个数据里有25个都突破了1 million的损失阈值,而且从假设检验来看是显著的突破了VaR,所以说这个VaR model是bad model。

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努力的时光都是限量版,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。

2024-10-05 14:14 1 · 回答

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