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wilsonxu · 2021年08月21日

这题不可以用cutoff来解释吗?

NO.PZ2016070202000002

问题如下:

A large, international bank has a trading book whose size depends on the opportunities perceived by its traders. The market risk manager estimates the one-day VAR, at the 95% confidence level, to be USD 50 million. You are asked to evaluate how good a job the manager is doing in estimating the one-day VAR. Which of the following would be the most convincing evidence that the manager is doing a poor job, assuming that losses are identical and independently distributed (i.i.d.)?

选项:

A.

Over the past 250 days, there are eight exceptions.

B.

Over the past 250 days, the largest loss is USD 500 million.

C.

Over the past 250 days, the mean loss is USD 60 million.

D.

Over the past 250 days, there is no exception.

解释:

D is correct. We should expect (195%)250=12.5{(1-95\%)}250=12.5 exceptions on average. Having eight exceptions is too few, but the difference could be due to luck. Having zero exceptions, however, would be very unusual, with a probability of 95%250, which is very low. This means that the risk manager is providing VAR estimates that are much too high. Otherwise, the largest or mean losses are not directly useful without more information on the distribution of profits.

老师好,本题解答用的mean=12.5天,作为判断标准;为什么不是用统计量作为判断标准,例如:95%的置信区间,统计量算出应该是19.2天(cutoff)。 用mean判断和用t统计量判断的区别是什么?谢谢!
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李坏_品职助教 · 2021年08月21日

嗨,努力学习的PZer你好:


首先这里的12.5不是mean,这个是一年交易日250天乘以(1-95%)算出来的12.5,这个是按照95%置信度水平下一年内理论上应当出现的exception次数。考虑var的exception的时候不要考虑统计量,只有在计算var具体数值的时候才需要考虑统计量。


var的意义是分析在置信度(95%)水平下,一段时期内最大损失不会超过多少钱。

这个经理算出来是50m,但是D项的过去250天里没出现一次超过50m的,这种概率等于是95%的250次方,概率太低了。由此可推测,经理算的var太大了,不准确。

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2022-11-03 14:17 1 · 回答

NO.PZ2016070202000002 如果说mean值超过了60m 那var值是50m 肯定是说明var低估了呀 那这个模型就不准确了呀

2021-03-05 19:01 1 · 回答

这里的Meloss是Expecteshortfall的意思吗

2020-11-01 14:02 1 · 回答