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Elsa陆艳 · 2022年03月31日

GARCH(1,1)里beta+alpha1+alpha0*VL=1

NO.PZ2016062402000047

问题如下:

A risk manager estimates daily variance hth_t using a GARCH model on daily return rt:ht=α0  +α1rt12+βht1,  with  α0=0.005,α1  =0.04,β=0.94r_t:h_t=\alpha_0\;+\alpha_1r_{t-1}^2+\beta h_{t-1},\;with\;\alpha_0=0.005,\alpha_1\;=0.04,\beta=0.94.

The long-run annualized volatility is approximately

选项:

A.

13.54%

B.

7.94%

C.

72.72%

D.

25.00%

解释:

The long-run mean variance is h=α01α1β=0.00510.040.94=0.25h=\frac{\alpha_0}{1-\alpha_1-\beta}=\frac{0.005}{1-0.04-0.94}=0.25. Taking the square root, this gives 0.5 for daily volatility. Multiplying by 252\sqrt{252}, we have an annualized volatility of 7.937%.

老师,我不理解为什么算出来的VL=025,也要开根号

1 个答案

品职答疑小助手雍 · 2022年03月31日

同学你好,因为求出来的VL=0.25是方差,开方才能得到标准差,也就是题目问的volatility。

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