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王雅轩 · 2022年12月23日

没太理解19

NO.PZ2018122701000034

问题如下:

A bank conducted a backtest of its 95% daily value at risk (VaR) and observed 19 exceptions - i.e., the number of days where the daily P&L loss exceeded the VaR - over the last year which included 250 trading days (T = 250). If we use the normal distribution to approximate the binomial for purposes of model verification, what is our accept/reject opinion of the model under a 90% two-tailed test?

选项:

A.

Accept with a test statistic of 1.25

B.

Accept with a test statistic of 1.89

C.

Reject with a test statistic of 1.25

D.

Reject with a test statistic of 1.89

解释:

D is correct.

考点 Backtesting VaR

解析 Null hypothesis is H0: Model is good with E[exceptions] = (1 - 95%) × 250 = 12.5 exceptions

The standard error (standard deviation) of the binomial variable = SQRT[p(1-p)T] = SQRT(5% × 95% × 250) = 3.446

The test statistic is [19 - 12.5] / 3.446 = 1.89

In words, we observed 6.5 more exceptions (19 - 12.5) than expected if the model is good, which is 1.89 standard deviations away from the expected number of exceptions. Since we know that a 95% one-tailed normal confidence interval implies a 1.645 cutoff, we know that 1.645 is also the cutoff for a 90% two-tailed since the normal is symmetrical, this falls outside the acceptance region. We reject the null, assuming that luck does not explain this, and find the model faulty.

请问老师19是哪里的来的呀

1 个答案

李坏_品职助教 · 2022年12月23日

嗨,爱思考的PZer你好:


19是题干给出的“observed 19 exceptions”,意思是一共有19个极端值。

理论上按照95%的置信度,应该是有12.5个极端值,但实际上观测到了19个,多出来6.5个。计算t统计量发现 [19 - 12.5] / 3.446 = 1.89,大于1.645,所以拒绝原假设。

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