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cenwandada · 2024年07月23日

这个公式是哪里的,需要记住吗

NO.PZ2023100703000032

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,


这个公式是哪里的,需要记住吗

1 个答案

品职答疑小助手雍 · 2024年07月23日

同学你好,这个也是extreme value theory那个章节的内容,不过2级不是很侧重计算,这种复杂的公式基本没考过,学有余力的情况下了解即可。

讲义里没有,原版书45页如下图:

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