Probability of exceptions

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.