
Explanation:
To determine if the model is well-calibrated, we perform a Kupiec test (two-tailed) or calculate the expected upper bound of exceptions using the normal approximation. The expected number of exceptions for a 98% VaR model over 252 days is:
The variance is: Standard deviation
Using a normal approximation for a 95% confidence level (two-tailed), the critical value . The upper limit of the non-rejection region is:
Since 10 is the first integer outside the non-rejection region ($10 > 9.39$), 10 daily losses will lead to the conclusion that the model is incorrectly calibrated.
Alternatively, using Kupiec's approximate test statistic with a 95% chi-square critical value of $3.841x = 10LR \approx \frac{(10 - 5.04)^2}{4.9392} = 4.98> 3.841$. Therefore, we reject the null hypothesis at 10 losses.
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Q.21 Michael Roy, a risk analyst at a large multinational bank, is backtesting the VaR model of the bank. The model being tested is a daily, 98% VaR model. If the backtest is conducted for one year at the 95% confidence level, and assuming 252 days in a year, what is the number of daily losses that will lead Roy to conclude that the model is not calibrated correctly?
A
8
B
9
C
10
D
5
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