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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.
**Explanation:** **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. This is known as the Gnenedenko-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 (not infinity), then the distribution of the original data could be a light-tail distribution such as normal or log-normal. In this case, 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-distribution, etc. EVT does not require the underlying distribution to be specifically normal or lognormal. **D is incorrect.** As the threshold value is decreased, the number of exceedances actually increases (not decreases), which can affect the reliability of parameter estimates. **Key EVT Concepts:** - **Extreme Value Theory (EVT)** focuses on modeling the tail behavior of distributions - **Generalized Pareto Distribution (GPD)** models exceedances over high thresholds - **Peaks-Over-Threshold (POT)** approach uses GPD to model extreme losses - **GPBdH Theorem** establishes the convergence to GPD for high thresholds
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The CRO of a regional bank expresses concern in a meeting of the risk team that the bank's internal risk models are not adequately assessing potential random extreme losses. A risk analyst asks if implementing a model based on extreme value theory (EVT) would address the CRO's concern. Which of the following is correct when applying EVT and examining distributions of losses exceeding a threshold value?
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.