1. Estimate the simple GARCH(1,1) model on the S&P 500 daily log returns using the maximum likelihood estimation (MLE) technique. First estimate

2t C1 D !CR2t C2t

; with Rt D tzt; and zt  N.0;1/

Let the variance of the first observation be equal to the unconditional variance, Var.Rt/:

Set the starting values of the parameters to D 0:1; D 0:85; and ! D Var.Rt/.1???? ????

/  0:012
0:05 D 0:000005. Reestimate the equation using variance targeting; that is, set

! D Var.Rt/.1???? ????/; and use Solver to find and only. Check how the estimated parameters and persistence differ from the variance model in Chapter 1.