问一道题：NO.PZ2016062402000012 [ FRM I ]

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 $V_2=\$100e^{0.10+1.96\times0.2}=\$100e^{0.492}=\$163.56$ .

老师能详细解释一下这道题吗

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1 个答案

小刘_品职助教 · 2021年03月08日

同学你好，

首先收益率r的分布是满足正态分布的，均值是0.1，sigma是0.2；

然后利用了s 和r 之间的关系， ln（s1/s0）=r

两边取对数之后就是s1/s0=e^r

求s的上下限其实就是求95%置信区间下的r的上下限，所以以上限为例，有

s1=100*e^(0.1+0.2*1.95)=163.56

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问一道题：NO.PZ2016062402000012 [ FRM I ]

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