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小宋宋 · 2021年05月11日

这个双尾检验没有搞明白

NO.PZ2016070202000006

问题如下:

Tycoon Bank announced that there were eight days in the previous year for which losses exceeded the daily 99% VAR. As a result, concerns emerged about the accuracy of the VAR implementation. Assuming that there are 250 days in the year, which of the following statements is/are correct?

I. Using a two-tailed 99% confidence level z-score test, the current VAR implementation understates the actual risk in the bank's portfolio.

II. Using a two-tailed 99% confidence level z-score test, the current VAR implementation overstates the actual risk in the bank's portfolio.

III. The bank's exception rates for VAR may be inaccurate if the bank's portfolio changes incorporate the returns from low-risk but highly profitable intraday market making activities.

IV. If these eight exceptions all happened in the previous month, the model should be reexamined for faulty assumptions and invalid parameters.

选项:

A.

I and III

B.

I, III, and IV

C.

Ill only

D.

I, II, and IV

解释:

  1. The z-score gives 82.5250×0.01×0.99=3.5\frac{8-2.5}{\sqrt{250\times0.01\times0.99}}=3.5 This is too high (greater than 2.58), which leads to rejection of the null that the VAR model is well calibrated. Hence, VAR is too low and statement I. is correct. Statement II. is incorrect. However, this may be due to intraday trading, so III. is correct, too. Finally, if all eight exceptions occurred in the last month, there is bunching, and the model should be reexamined, so IV. is correct.

当VaR 天数越大,那算出来p-value 大 月会就拒绝,怎么是 overestimate ,明明是underestimate ma

1 个答案

品职答疑小助手雍 · 2021年05月11日

嗨,从没放弃的小努力你好:


最直观的角度:目前银行的模型算出来一个var,现在是在检验这个var大了还是小了,按理说99%的var,期望是一年250天中有2.5天超过这个var,现在有8天的损失都超过了这个var,那显然这个模型估计的var小了,所以说公司的模型underestimate 了var。

解析的角度,模型的接受域是在2.5天+-2.58倍的标准差的范围内的,现在p value大于了2.58,也就落在了接受域之外,也就是超过的天数太多了,超过天数太多的原因就是模型设定的var太小了。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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