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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-deHaan (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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During a risk team meeting, the Chief Risk Officer (CRO) of a regional bank expressed concerns regarding the inadequacy of the bank's current risk models in assessing potential random extreme losses. In response, a risk analyst suggested the incorporation of a model based on extreme value theory (EvT) to address this problem. Considering the use of EvT and focusing on the analysis of loss distributions that exceed a specific threshold, which of the following statements holds true?
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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