GARCH(1,1) Model

FRM
#1

Assume an analyst uses daily data to estimate a GARCH(1,1) model as follows: covn = 0.000002 + 0.l4Xn_1Yn_1 +0.76cov n_ 1 The analyst also determines that the estimate of covariance on day n — 1 is 0.018 and the most recent observation on covariance is 0.02 .What is the updated estimate of covariance?

Answer: The updated estimate of covariance on day n is 0.0304%, which is calculated as: covn = 0.000002 + (o. 14 x 0.02^2) + (o.76 x 0.0182^2) = 0.000002 + 0.000056 + 0.000246 = 0.000304 I don’t understand why is 0.02^2 and 0.0182^2 and not 0.02 and 0.0182 because base on the formula generalized autoregressive conditional heteroskedasticity (GARCH) model they are without exponent.

#2

When any model captures non linear changes then it genrally uses square terms and later standardize it by taking square root.

In, garch we are estimating new / updated volatility therefore we need to capture the non linear changes.