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薛真 · 2020年03月23日

问一道题: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.

为什么不是用INSt服从正态分布的那个公式做呢

4 个答案

袁园_品职助教 · 2020年04月07日

同学你好!

这里计算一天的标准差就是用的 σ/根号T 这个公式啊~

不知道有没有解答你的疑问

薛真 · 2020年04月04日

袁园_品职助教 · 2020年03月30日

同学你好!

你一直提到的书上的公式可否截个图看一下?

这里的解题思路还是挺清晰的,求区间就先求 μ 和 sigma,先把题目中的这两个条件从年化转换成天化,μ 直接除以天数,sigma 用平方根法则除以 根号下天数。

如果你还有问题可以继续提问~

袁园_品职助教 · 2020年03月24日

同学你好!

一般短期(例如本题是 one day)就利用μ服从正态分布来计算,长期(例如月度、年度)就利用lnSt来计算。

薛真 · 2020年03月30日

另外,书上给的标准差公式是σ/根号T,我看这里算的应该是直接用平方根法则了,是吗?为什么不用书上的公式,计算完了以后再用平方根法则。,另外,书上的公式涉及的参数T的单位是年吗?

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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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2023-06-08 22:56 1 · 回答

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