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跟上一题的结论是冲突的啊

NO.PZ2016062402000046

问题如下：

Assume you are using a GARCH model to forecast volatility that you use to calculate the one-day VAR. If volatility is mean reverting, what can you say about the T-day VAR?

选项：

It is less than the $\sqrt T\times$ one-day VAR.

It is equal to $\sqrt T\times$ one-day VAR.

It is greater than the $\sqrt T\times$ one-day VAR.

It could be greater or less than the $\sqrt T\times$ one-day VAR

解释：

If the initial volatility were equal to the long-run volatility, then the T-day VAR could be computed using the square root of time rule, assuming normal distributions. If the starting volatility were higher, then the T-day VAR should be less than the $\sqrt T\times$ one-day VAR. Conversely, if the starting volatility were lower, then the T-day VAR should be more than the long-run value. However, the question does not indicate the starting point. Hence, answer d. is correct.

上一题明明是小于根号下T天的波动率，这题就变成即可大于也可小于了

同学你好，

PZ2016062402000043：由于均值复归的特性，长期来看天然气的价格应该在均值周围波动，即长期的波动率比较小，用平方根法则把长期波动率转换为日波动率相应也就小，因此计算的VAR也小。

PZ2016062402000046：如果初始的波动率=长期波动率，那么因为它有均值回归的特点，之后每天的波动率都等于长期的波动率也就等于现在的波动率，VaR可以使用平方根法则；如果现在的波动率小于长期波动率，那么根据均值回归的特点，它之后的波动率会慢慢回归，也就是要变大。波动率要慢慢变大，那么VaR也就要慢慢变大。就会大于最开始的VaR乘上根号n。反之，也是一样的道理。所以选D。

这两题本质的区别是第一题是有一种宏观转微观的感觉，长期转为1天（包含了从低到高从高到低的周期过程），如果均值复归特性的话长期波动的估计会小一些，导致通过平方根法则会使日的也变小；而第二题是微观估微观的感觉，1天变几天那种情况（处于周期中的一段），但是由于无法判断属于均值复归周期中的哪一段，所以无法判断升高还是降低。

跟上一题的结论是冲突的啊

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