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 $S=100\times e^r$, 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：

$67.57 and $147.99

$70.80 and $149.20

$74.68 and $163.56

$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 $100$e^{\mu\pm\alpha\sigma}$ The lower limit is then $V_1=\$100e^{0.10-1.96\times0.2} =\$100e^{-0.292}=\$74.68$. The upper limit is $V_2=\$100e^{0.10+1.96\times0.2}=\$100e^{0.492}=\$163.56$.