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magickame · 2021年09月30日

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:


 

A.

It is less than the T×\sqrt T\timesone-day VAR.

B.

It is equal to T×\sqrt T\timesone-day VAR.

C.

It is greater than the T×\sqrt T\timesone-day VAR.

D.

It could be greater or less than the T×\sqrt T\timesone-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 T×\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

1 个答案

品职答疑小助手雍 · 2021年10月02日

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。

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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?

2024-06-26 14:29 2 · 回答

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。

2021-11-01 16:49 2 · 回答

NO.PZ2016062402000046 没有理解这道题的

2021-09-27 20:32 1 · 回答

不是说 均值复归则ρ<0,那么算出的σ是会小于均值复归的σ,VAR也是如此吗?

2020-03-09 19:03 2 · 回答