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A CRO is concerned that existing internal risk models of a firm, which are governed mainly by the central limit theorem, are not adequate in addressing potential random extreme losses of the firm. The CRO then recommends the use of extreme value theory (EVT). When applying EVT and examining distributions of losses exceeding a threshold value, which of the following is correct?

A) As the threshold value is increased, the distribution of losses over a fixed threshold value converges to a generalized Pareto distribution.》》》想了解更多21年FRM備考技巧的點我咨詢?

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.

答案:A

進群領資料

解析:A key foundation of EVT Is that as the threshold value is increased, the distribution of loss exceedances converges to a generalized Pareto distribution.【資料下載】FRM一級思維導圖PDF版

Assuming the threshold is high enough, excess losses can be modeled using the generalized Pareto distribution. Thus, Ais correct. 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.

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