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比如世界 · 2020年04月01日

问一道题:NO.PZ2016062402000012

问题如下:

Consider a stock with an initial price of $100. Its price one year from now is given by S=100×erS=100\times e^r, where the rate of return r is normally distributed with a mean of 0.1 and a standard deviation of 0.2. With 95% confidence, after rounding, S will be between

选项:

A.

$67.57 and $147.99

B.

$70.80 and $149.20

C.

$74.68 and $163.56

D.

$102.18 and $119.53

解释:

Note that this is a two-tailed confidence band, so that α = 1.96. We find the extreme values from $100eμ±ασe^{\mu\pm\alpha\sigma} The lower limit is then V1=$100e0.101.96×0.2=$100e0.292=$74.68V_1=\$100e^{0.10-1.96\times0.2} =\$100e^{-0.292}=\$74.68. The upper limit is V2=$100e0.10+1.96×0.2=$100e0.492=$163.56V_2=\$100e^{0.10+1.96\times0.2}=\$100e^{0.492}=\$163.56.

老师您好,突然有个疑问,那几个特殊点对应的区间是针对于标准正态分布的还是正态分布?谢谢

1 个答案

袁园_品职助教 · 2020年04月02日

同学你好!

是所有的正态分布