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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.
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A Chief Risk Officer (CRO) is concerned that the company's existing internal risk assessment models may not adequately manage potential unexpected substantial losses. To address this, the CRO proposes the application of Extreme Value Theory (EVT). When using EVT to examine the distributions of losses that exceed a specific threshold, what is the correct methodology to follow?
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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