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JiangHan · 2023年04月10日

GARCH模型

NO.PZ2019040801000079

问题如下:

Anlyst Pengyu is using a GARCH(1,1) model to estimate daily variance on daily returns(rt) :

ht:=α0 + α1r2t-1 + βht-1   

while α0 = 0.000003

α1 = 0.03

β = 0.94

What is the long-run annualized volatility estimate (assuming that volatility increases by the square root of time and 252 trading days in a year ?

选项:

A.

0.015%.

B.

1.00%.

C.

9.27%.

D.

15.87%.

解释:

D is correct.

考点:GARCH(1,1)模型

解析:首先求出γ,GARCH(1,1)中α1+β+γ=1,所以γ=1-0.03-0.94=0.03.

然后long-run daily variance= α0 / γ= 0.000003/0.03= 0.0001

那么波动率就是标准差,用方差开方即可:0.01.

最后年化0.01*(252^0.5)=15.87%

lLongrun daily standard deviation =variance=0.00004=0.6325%Annualized standard deviation=daily standard deviation×time=0.6325%×252=10.04%{l}Long-run\text{ }daily\text{ }standard\text{ }deviation\text{ }=\sqrt{variance}=\sqrt{0.00004}=0.6325\%\\Annualized\text{ }standard\text{ }deviation=daily\text{ }standard\text{ }deviation\times\sqrt{time}\\=0.6325\%\times\sqrt{252}=10.04\%

老师这个知识点有点忘了,可以具体解释一下这个题吗,γ是什么,variance是怎么算出来的

1 个答案

pzqa27 · 2023年04月11日

嗨,从没放弃的小努力你好:


γ是方差的系数,用到的就是GARCH的定义式,已知γ*VL=α0=0.000003,又因为α1+β+γ=1,所以VL=0.0001

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