Consider the following GARCH(1,1) model for the volatility of asset returns ๐ ๐ก : ๐ ๐ก = ๐ผ + ๐ฝ ๐ ๐ก โ 1 + ๐ ๐ก ๐ ๐ก = โ ๐ก ๐ข ๐ก โ ๐ก = ๐ + ๐ฟ โ ๐ก โ 1 + ๐ ๐ ๐ก โ 1 2 ๐ผ ๐ก โ 1 ( ๐ข ๐ก ) = 0 ๐ผ ๐ก โ 1 ( ๐ข ๐ก 2 ) = 1 You estimated the following values for the parameters Estimates Parameters ๐ผ ๐ฝ ๐ ๐ฟ ๐ Estimates 0.111 0.8122 0.0011 0.9321 0.0511 Assume that the last 2 observations of the return process are ๐ ๐ = 0.27 and ๐ ๐ โ 1 = 0.02 , and the value of the conditional variance in the last period of your sample is โ ๐ = 0.75 . Then what is the predicted value of the conditional variance โ ๐ + 1 in period ๐ + 1 ? Single choice
A
โ ฬ ๐ + 1 = 0.0729
B
โ ฬ ๐ + 1 = 0.701216
C
There is not enough data to compute โ ฬ ๐ + 1 .
D
โ ฬ ๐ + 1 = 0.519615
E
โ ฬ ๐ + 1 = 0.866025
F
โ ฬ ๐ + 1 = 0.75
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On Tuesday, you calculated the volatility of Wednesday as 5% using the GARCH model, which information will make the Thursday volatility become even higher?
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