Explanation:
To determine whether the VaR model is well-calibrated, we perform a Kupiec test or analyze the binomial distribution of exceptions.
The expected number of exceptions is N × p = 252 × 0.005 = 1.26.
We evaluate the cumulative probability of observing exactly X exceptions using the binomial distribution (N=252, p=0.005):
The cumulative probability P(X ≤ 4) ≈ 99.1%. Thus, the probability of observing 5 or more exceptions is P(X ≥ 5) = 1 - P(X ≤ 4) = 1 - 0.991 = 0.009 (0.9%).
Because the test is conducted at a 99% confidence level (which corresponds to a 1% significance level for rejection in the upper tail), observing 5 exceptions falls into the < 1% tail and would lead to rejecting the model. Observing 4 exceptions has an upper tail probability of roughly 3.9%, which is > 1% and therefore acceptable. Therefore, the maximum acceptable number of exceptions is 4.
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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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