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Elsa陆艳 · 2022年02月21日

老师,不太理解这个去年化的折算,用lnSt~N的公式应该怎么做呢?

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.

老师,不太理解这个去年化的折算,用lnSt~N的公式应该怎么做呢?

1 个答案

品职答疑小助手雍 · 2022年02月21日

同学你好,这里完全不会用到 ln 。

做题过程就是先通过年化收益率和波动率,把日的收益率和波动率算出来。

然后波动率加减0.995正态分布对应的分位点*波动率就可以得到结果了。


收益率是直接除以252,波动率是除以根号下252,分位点就是类似1.96, 1.645那种查表可以得到的分位点。

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