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Ella · 2024年10月31日

这题的知识点在哪

NO.PZ2023100703000034

问题如下:

A risk analyst at an investment bank is evaluating the bank’s application of extreme value theory (EVT) in managing financial risks. The analyst compares different methods of estimating extreme value (EV) parameters for the bank’s operational loss distribution and examines the mechanics of each method, as well as their advantages and disadvantages. Which of the following statements regarding a method used for estimating EV parameters is correct?

选项:

A.The regression method uses an ordered sample of losses to obtain least squares estimates of the EV parameters. B.The maximum-likelihood method uses the average of a random number of the most extreme observations to estimate EV parameters. C.The main challenge associated with the moment-based method is choosing the number of observations that minimizes the mean-squared-error loss function. D.A drawback of the semi-parametric estimation method is that the Hill estimator is neither consistent nor asymptotically normal.

解释:

A is correct. The regression method is the easiest method to apply, and the recovery of least squares estimates of the EV parameters from a regression is straightforward. The first step in applying the regression method is to order the sample of extreme values from lowest to highest. B is incorrect. The use of an arbitrary (not random) number would correctly describe the Hill estimator, which is used in semi-parametric estimation method. However, this would still be an incorrect answer to this specific question. C is incorrect. The main challenge with the semi-parametric method (not the moment-based method) is choosing the number of observations to include in the tail, as the parameter estimates can be sensitive to this number. D is incorrect. The most popular semi-parametric estimation method is the Hill estimator, which is known to be consistent and asymptotically normal.

这题的知识点在哪

1 个答案
已采纳答案

李坏_品职助教 · 2024年10月31日

嗨,爱思考的PZer你好:


本题考查的是估计EV parameters 的不同方法。可以参考FRM原版书里面“Estimation of EV Parameters”这个部分的内容:

regression就回归模型,回归模型是用最小二乘法得出最后的参数估计值,A选项正确。


而Semi-Parametric方法:

这个方法里面的Hill estimator是满足一致性(consistent)的,D选项说Hill不满足一致性,所以D错误。


而Maximum Likelihood这个是极大似然估计:

这个方法是找到使概率函数最大的参数估计值,不是随机数(random number),B选项错误。


C选项说的moment based method的缺点是:

C选项里面说的并不是该方法的缺陷。




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2024-08-16 15:56 1 · 回答