老师，均值复归不应该是两个方向吗？

NO.PZ2016062402000043

问题如下：

Assume we calculate a one-week VAR for a natural gas position by rescaling the daily VAR using the square root of time rule. Let us now assume that we determine the true gas price process to be mean reverting and recalculate the VAR. Which of the following statements is true?

选项：

The recalculated VAR will be less than the original VAR.

The recalculated VAR will be equal to the original VAR.

The recalculated VAR will be greater than the original VAR.

There is no necessary relationship between the recalculated VAR and the original VAR.

解释：

With mean reversion, the volatility grows more slowly than the square root of time.

均值复归既可以向上也可以向下回归，为什么这道题就能肯定是向下呢？

Original VaR=weekly VaR

Resceduled VaR=根号7 * 1天的VaR

怎么比较大小呢

烦请老师解答，谢谢！

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DD仔_品职助教 · 2022年02月11日

嗨，爱思考的PZer你好：

同学你好，

这跟均值复归的方向没有任何关系呀，无论是向上还是向下，都是往均值走，都是在均值附近进行波动，这种情况σ也就是volatility会变得更小，Var就是根据σ进行计算出来的，那么σ小，根据均值复归计算出来的var也就会更小。

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努力的时光都是限量版，加油！

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Brian邵彬 · 2024年06月26日

上一道题，我记得有个回复是这么说的： “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： 1）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。 2）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。所以这道题为什么一定是less than呢？

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NO.PZ2016062402000043 问题如下 Assume we calculate a one-week VAR for a naturgposition rescaling the ily Vusing the square root of time rule. Let us now assume thwe termine the true gpriprocess to be mereverting anrecalculate the VAR. Whiof the following statements is true? The recalculateVwill less ththe originVAR. The recalculateVwill equto the originVAR. The recalculateVwill greater ththe originVAR. There is no necessary relationship between the recalculateVanthe originVAR. With mereversion, the volatility grows more slowly ththe square root of time. σ 周=根号下5*σ 天，σ 周 σ 天，1-σ变大，在return的正态分布图上，VaR条线就往左移，面积就变小。这么理解对吗？

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2020-09-05 16:30 1 · 回答

老师，均值复归不应该是两个方向吗？

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