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海胆君 · 2021年03月20日

为什么用N(0.995)??不是99%CI吗?

NO.PZ2020021205000060

问题如下:

A stock has an expected return of 15% and a volatility of 20%. The current price of the stock is USD 50. Estimate a 99% confidence interval for the price at the end of one day.

选项:

解释:

Here, we are dealing with a short time period, and so it is reasonable to assume that the return is normally distributed. The return has a mean of 15% X (1 /252) = 0.0595%, and a standard deviation of 20% X 1/252\sqrt{1/252} = 1.2599%. The 99% confidence interval for the percentage return is between:

0.0595 - 1.2599 X N1N^{-1}(0.995) = -3.186%

and

0.0595 + 1.2599 X N1N^{-1}(0.995)= +3.305%

The confidence interval for the stock price is therefore between 50 X 0.96814 = 48.4 and

50 X 1.03305 = 51.7.

计算中,是采用Return~N来算的,return不是可正可负吗那为什么要把99%置信区间换成99.5%?这是双尾变单尾???不是可正可负吗

2 个答案
已采纳答案

品职答疑小助手雍 · 2021年03月21日

嗨,爱思考的PZer你好:


这个N负一次方的公式代表的是正态分布累计概率的反函数,现在你要求的是一个中间区间占了99%的区间,也就是区间两边各剩下0.5%的概率。

那你用的分位点应该是累计了0.5%和99.5%概率的两个点。这题是要双尾查表,但是N负一次方那个函数是一直累计的那种函数(换言之它是单尾的)。


如果前面你还是看不懂,那就只能记住,正态分布里单尾0.995和双尾的0.99是一样的,N那个公式里面对应的都是单尾数值。

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海胆君 · 2021年03月21日

理解了 谢谢!

品职答疑小助手雍 · 2021年03月20日

嗨,从没放弃的小努力你好:


用的是单边99.5%分位点,两边各0.5%,中间部分就是99%了。

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努力的时光都是限量版,加油!

海胆君 · 2021年03月20日

没听懂……不是说先判断单双边再查表吗? 那这个就应该是找的N(0.99)啊

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NO.PZ2020021205000060 问题如下 A stohexpectereturn of 15% ana volatility of 20%. The current priof the stois US50. Estimate a 99% confinintervfor the prithe enof one y. Here, we are aling with a short time perio anso it is reasonable to assume ththe return is normally stribute The return ha meof 15% X (1 /252) = 0.0595%, ana stanrviation of 20% X 1/252\sqrt{1/252}1/252​ = 1.2599%. The 99% confinintervfor the percentage return is between:0.0595 - 1.2599 X N−1N^{-1}N−1(0.995) = -3.186%an.0595 + 1.2599 X N−1N^{-1}N−1(0.995)= +3.305%The confinintervfor the stopriis therefore between 50 X 0.96814 = 48.4 an0 X 1.03305 = 51.7. The confinintervfor the stopriis therefore between 50 X 0.96814 = 48.4 an0 X 1.03305 = 51.7.老师,上面这个一步想确认一下,是分别用50*exp(-3.186%) 、50*exp(+3.305%)吗?

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