1、We are doing a backtest of VaR model according to Basel II. Assume the bank’s 10-day 99% VaR is $1 million. The null hypothesis is: the VaR model is accurate. Out of 1,000 observations, 25 exceptions are observed (Binomial CDF )
A. We will probably call the VaR model good but risk a Type I error.
B. We will probably call the VaR model good but risk a Type II error.
C. We will probably call the model bad but risk a Type I error.
D. We will probably call the model bad but risk a Type II error.
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.
2、In backtesting a value at risk (VaR) model that was constructed using a 90% confidence level over a 250-day period, how many exceptions are forecasted?
(1 – 0.90) × 250 = 25