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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年06月08日

99% confidence interval for the percentage return算法?

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.

我算出来的 99% confidence interval for the percentage return is between:

  • 0.0595%+2.33*1.2599%=2.995%
  • 0.0595%-2.33*1.2599%=-2.876%


为什么跟解析不一样?

1 个答案
已采纳答案

pzqa27 · 2023年06月09日

嗨,从没放弃的小努力你好:


不应该带入2.33,应该使用2.58

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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?

2024-10-17 14:18 1 · 回答

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2024-09-04 10:41 1 · 回答

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2024-08-06 00:46 1 · 回答

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2023-03-28 21:13 1 · 回答