
Explanation:
The problem requires finding the maximum number of exceptions without rejecting the VaR model using a binomial distribution.
Here, the number of trials , and the probability of exception .
The expected number of exceptions .
Using the Poisson approximation or exact binomial probabilities, we calculate the cumulative probabilities:
P(X = 0) = 0.283
P(X = 1) = 0.358
P(X = 2) = 0.226
P(X = 3) = 0.095
P(X = 4) = 0.030
Summing these up:
P(X 0) = 0.283 P(X $\le\le$2) = 0.867
P(X 3) = 0.962 P(X $\lecP(X \le c) \ge 0.99P(X \le 4) \approx 0.992$, up to 4 exceptions are acceptable. If 5 or more exceptions occur, the model is rejected. Thus, the maximum acceptable number of losses exceeding the VaR is 4.
Q.51 Paul Ferguson, FRM, works as an analyst at a U.S. based bank. He wishes to test the bank’s 1-day 99.5% VaR model over a 1-year horizon at a 99% confidence level. Assuming 252 days in a year, determine the maximum number of daily losses exceeding the 1-day 99.5% VaR that’s acceptable to conclude that the model is well calibrated.
A
2
B
3
C
4
D
0
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