这个公式是哪里的，需要记住吗

问题如下：

An investment bank with an active position in commodity futures is using the peaks-over-threshold (POT) methodology for estimating VaR and ES. The bank’s risk managers have set a threshold level of 3.00% to evaluate excess losses. The choice of the threshold, they argue, is suitable and consistent with the finding that 5.00% of the observations are in excess of the threshold value. The risk managers have concluded that the position’s VaR using the POT measure is 4.45% at 99% confidence level. The VaR estimate incorporates the following assumptions generated from the managers’ empirical analysis:

Given the VaR value and the parameter assumptions, which of the following is correct?

选项：

A.Increasing the value of the tail index lowers both the ES and the VaR

B.Increasing the loss threshold level increases both the ES and the VaR

C.The value of ES is 4.57%

D.The value of ES is 5.71%

解释：

B is correct (as can beseen from the formula below), increasing u increases both VaR and ES even if nmay be lower as u increases.

A is incorrect. Increasingthe tail parameter value actually increases both VaR and ES.

C and D are incorrect. Accordingto the peaks-over-threshold (POT) risk measure, the VaR and ES (in percentage)are computed by (note: the first equation is not necessary as the value of VaR isgiven):

and,

Therefore,