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