Consider the following GARCH(1,1) model for the volatility of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝛼 + 𝛽 𝑟 𝑡 − 1 + 𝜀 𝑡 𝜀 𝑡 = ℎ 𝑡 𝑢 𝑡 ℎ 𝑡 = 𝜇 + 𝛿 ℎ 𝑡 − 1 + 𝜙 𝜀 𝑡 − 1 2 𝔼 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔼 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 You estimated the following values for the parameters Estimates Parameters 𝛼 𝛽 𝜇 𝛿 𝜙 Estimates 0.111 0.8122 0.0011 0.9321 0.0511 Assume that the last 2 observations of the return process are 𝑟 𝑇 = 0.27 and 𝑟 𝑇 − 1 = 0.02 , and the value of the conditional variance in the last period of your sample is ℎ 𝑇 = 0.75 . Then what is the predicted value of the conditional variance ℎ 𝑇 + 1 in period 𝑇 + 1 ? 单项选择题

A

ℎ ̂ 𝑇 + 1 = 0.0729

B

ℎ ̂ 𝑇 + 1 = 0.701216

C

There is not enough data to compute ℎ ̂ 𝑇 + 1 .

D

ℎ ̂ 𝑇 + 1 = 0.519615

E

ℎ ̂ 𝑇 + 1 = 0.866025

F

ℎ ̂ 𝑇 + 1 = 0.75

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