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Olivia Chen · 2020年10月11日

问一道题:NO.PZ2016062402000047 [ FRM I ]

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%.

老师可以讲下这个题目和知识点吗
2 个答案

品职答疑小助手雍 · 2022年03月31日

已经在提问里回答过啦~

品职答疑小助手雍 · 2020年10月12日

嗨,爱思考的PZer你好:


GARCH(1,1)里beta+alpha1+alpha0*VL=1,这个定义结论要记牢。

已知其他三项,反求VL即可。

 


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Elsa陆艳 · 2022年03月31日

是啊,我有点不太理解的是为什么VL要开根号,252天的平方根法则我知道的

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NO.PZ2016062402000047问题如下A risk manager estimates ily varianhth_tht​ using a GARmol on ily return rt:ht=α0  +α1rt−12+βht−1,  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=0.94rt​:ht​=α0​+α1​rt−12​+βht−1​,withα0​=0.005,α1​=0.04,β=0.94.The long-run annualizevolatility is approximately 13.54% 7.94% 72.72% 25.00% The long-run mevarianis h=α01−α1−β=0.0051−0.04−0.94=0.25h=\frac{\alpha_0}{1-\alpha_1-\beta}=\frac{0.005}{1-0.04-0.94}=0.25h=1−α1​−βα0​​=1−0.04−0.940.005​=0.25. Taking the square root, this gives 0.5 for ily volatility. Multiplying 252\sqrt{252}252​, we have annualizevolatility of 7.937%.老师,我不理解为什么算出来的VL=025,也要开根号

2022-03-31 18:23 1 · 回答

NO.PZ2016062402000047 7.94% 72.72% 25.00% The long-run mevarianis h=α01−α1−β=0.0051−0.04−0.94=0.25h=\frac{\alpha_0}{1-\alpha_1-\beta}=\frac{0.005}{1-0.04-0.94}=0.25h=1−α1​−βα0​​=1−0.04−0.940.005​=0.25. Taking the square root, this gives 0.5 for ily volatility. Multiplying 252\sqrt{252}252 ​, we have annualizevolatility of 7.937%.求出来是ily,但是我不理解为什么✖️更号下252。为什么加更号

2022-01-23 21:35 1 · 回答

7.94% 72.72% 25.00% The long-run mevarianis h=α01−α1−β=0.0051−0.04−0.94=0.25h=\frac{\alpha_0}{1-\alpha_1-\beta}=\frac{0.005}{1-0.04-0.94}=0.25h=1−α1​−βα0​​=1−0.04−0.940.005​=0.25. Taking the square root, this gives 0.5 for ily volatility. Multiplying 252\sqrt{252}252 ​, we have annualizevolatility of 7.937%.想问一下这里的单位问题,0.5乘以根号下252确实等于7.93,但是为什么就变成了7.93%呢?那个百分号如何得到的

2020-03-03 10:30 1 · 回答

计算时,为啥r t-1和ht-1都变为1了?

2019-11-14 14:38 2 · 回答