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Answer: As the threshold value is increased, the distribution of losses over a fixed threshold value converges to a generalized Pareto distribution.
A is correct. A key foundation of EVT is that as the threshold value is increased, the distribution of loss exceedances converges to a generalized Pareto distribution. Assuming the threshold is high enough, excess losses can be modeled using the generalized Pareto distribution. It is known as the Gnedenko-Pickands-Balkema-de Haan (GPBdH) theorem and is heavily used in the peaks-over-threshold (POT) approach. B is incorrect. If the tail parameter value of the generalized extreme-value (GEV) distribution goes to zero, and not infinity, then the distribution of the original data (not the GEV) could be a light-tail distribution such as normal or log-normal. In other words, the corresponding GEV distribution is a Gumbel distribution. C is incorrect. To apply EVT, the underlying loss distribution can be any of the commonly used distributions: normal, lognormal, t, etc. D is incorrect. As the threshold value is decreased, the number of exceedances increases.
Author: LeetQuiz Editorial Team
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A Chief Risk Officer (CRO) expresses concern about the adequacy of the company's current risk assessment models in handling potential significant and unexpected losses. To address this issue, the CRO proposes the adoption of Extreme Value Theory (EVT). Considering the application of EVT and its focus on evaluating loss distributions that exceed a specified threshold, which of the following statements is correct?
A
As the threshold value is increased, the distribution of losses over a fixed threshold value converges to a generalized Pareto distribution.
B
If the tail parameter value of the generalized extreme-value (GEV) distribution goes to infinity, then, the GEV essentially becomes a normal distribution.
C
To apply EVT, the underlying loss distribution must be either normal or lognormal.
D
The number of exceedances decreases as the threshold value decreases, which causes the reliability of the parameter estimates to increase.
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