依据GARCH计算第10天volatility

问题如下：

Suppose that the current volatility estimate is 3% per day and the long-run average volatility estimate is 2% per day. What are the volatility estimates in ten days and 100 days in a GARCH (1,1) model where ω= 0.000002, α= 0.04, and β= 0.94?

解释：

The expected variance rate in ten days is 0.02^2 + (0.04 + 0.94)^10 (0.03^2– 0.02^2) = 0.000809, which corresponds to a volatility of 2.84%. The expected variance rate in 100 days is 0.02^2 + (0.04 + 0.94)^100 (0.03^2 – 0.02^2) = 0.000466, which corresponds to a volatility of 2.16%.

题目问：现在是volatility=3%，long-run average volatility=2%，利用GARCH(1，1)来计算10天和100天的volatility，ω= 0.000002, α= 0.04, and β= 0.94。

10天volatility=[0.02^2 + (0.04 + 0.94)^10 (0.03^2– 0.02^2)]^0.5 = 2.84%.

100天volatility=[0.02^2 + (0.04 + 0.94)^100 (0.03^2 – 0.02^2)]^0.5 = 2.16%.