请解释下这道题的考点和答案

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.

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李坏_品职助教 · 2021年09月27日

嗨，爱思考的PZer你好：

这道题问的是，如果波动率（其实就是标准差）带有mean-reverting（均值回归）的性质，就是说标准差不会偏离Long-term volatility太多。

因为题目里没有说一开始波动率处在什么位置，存在两种可能：

假如一开始波动率高于Longer-term volatility，那么T天的波动率应该会下降。我们计算的σ*√T是按照目前过高的波动率σ算出来的，所以真实的T-day σ应该会比σ*√T低一些。
假如一开始波动率低于Longer-term volatility，那么T天的波动率应该会上升。我们计算的σ*√T是按照目前过低的波动率σ算出来的，所以真实的T-day σ应该会比σ*√T高一些。

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NO.PZ2016062402000046 问题如下 Assume you are using a GARmol to forecast volatility thyou use to calculate the one-y VAR. If volatility is mereverting, whcyou sabout the T-y VAR? A.It is less ththe T×\sqrt T\timesT×one-y VAR. B.It is equto T×\sqrt T\timesT×one-y VAR. C.It is greater ththe T×\sqrt T\timesT×one-y VAR. It coulgreater or less ththe T×\sqrt T\timesT×one-y V If the initivolatility were equto the long-run volatility, then the T-y Vcoulcomputeusing the square root of time rule, assuming normstributions. If the starting volatility were higher, then the T-y Vshoulless ththe T×\sqrt T\timesT× one-y VAR. Conversely, if the starting volatility were lower, then the T-y Vshoulmore ththe long-run value. However, the question es not incate the starting point. Hence, answer is correct. 老师讲课的时候，不是说出现mereverting的话，T日的标准差直接用平方根法则计算的标准差么，原因是correlation 0。而如果是由tren话，则是T日的标准差直接用平方根法则计算的标准差。原因是correlation 0。T日标准差会变得越来越大。具体到这道题，既然是mereverting的特点，那不就应该是T日的标准差直接用平方根法则计算的标准差么？

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NO.PZ2016062402000046 其中一个老师的解答中，提到目前的价格可能是高于也可能是低于均值的，所以计算的volatility也就变大或者变小，导致VAR变大或者变小。那么那个天然气的题目中，是不是目前的价格也可以大于或者小于均值呢？这两种思路不矛盾么？烦请老师解答。

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NO.PZ2016062402000046 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

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请解释下这道题的考点和答案

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