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yanan · 2024年10月01日

解析看不懂,能详细说一下这题四个选项吗

NO.PZ2023100703000038

问题如下:

You are backtesting a bank’s VaR model. Currently, the bank calculates a 1-day VaR at the 99% confidence level, and you are recommending that is switch to a 95% confidence level. Which of the following statements concerning this switch is correct?

选项:

A.The 95% VaR model is less likely to be rejected using backtesting than the 99% VaR model. B.When validating with backtesting at the 90% confidence level, there is a smaller probability of incorrectly rejecting a 95% VaR model when it is valid than a 99% VaR model. C.The decision to accept or reject a VaR model based on backtesting results is more reliable with a 95% confidence level VaR model than with a 99% confidence level model. D.When backtesting using a 90% confidence level, there is a smaller probability of committing a type I error when backtesting a 95% VaR model than with a 99% VaR model.

解释:

The concept tested here is the understanding of the difference between the VaR parameter for confidence (here, namely 95% vs 99%) and the validation procedure confidence level, and how they interact with one another. Using a VaR confidence level creates a narrower rejection region by allowing a greater number of exceptions to be generated. This in turn increases the power of the backtesting process and makes for a more reliable test.

同学的提问和老师的回答也有点没明白,谢谢

1 个答案

pzqa27 · 2024年10月08日

嗨,努力学习的PZer你好:


题目说你在对一家银行的 VaR 模型进行回溯测试。目前,该银行按 99% 的置信水平计算 1 天的 VaR,而您建议改用 95% 的置信水平。关于这一转换,以下哪项陈述是正确的?

首先来看A选项使用backtesting时,95% VaR 模型比 99% VaR 模型被拒绝的可能性更小。这个是不对的。回测的confidence level都是95%,因此它们俩被拒绝的概率是一样的。

B选项说如果把回测的confidence level改成90%,拒真的概率在95%的VaR比99%VaR要低,拒真的概率是1类错误的概率,它就是回测的拒绝域的概率,就是1-90%=10%, 因此95%的VaR和99%VaR是一样的。

D选项跟B说的是一个意思,所以B错了D肯定也错了。

C.说根据backtesting结果决定接受或拒绝 VaR 模型,95% 置信度 VaR 模型比 99% 置信度模型更可靠。95%的var的接受域更窄,那么拒绝域更多,会有更多的exception作为对模型的考量。比如250个检测样本,对于99%VaR可能只有一两个损失超过了VaR,而对于95%的VaR却会有更多的超过VaR的数,所以这个backtesting过程会更可靠一些。

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