Can someone provide a typical numerical values of GARCH(1,1) coefficients $(\omega,\alpha,\beta)$ for estimating SPX index variance? I will appreciate it if some references could be provided.
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$\begingroup$ $\alpha$ somewhere in the vicinity of 0.1, $\beta$ close to $0.9$. $\omega=\sigma_{LR^2}(1-\alpha-\beta)$ where $\sigma_{LR}^2$ is the long-run variance. $\endgroup$– Richard HardyNov 24, 2017 at 19:37
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$\begingroup$ @RichardHardy: Thank you. I agree with the rough range you listed. However, I would prefer a bit more precision for all the parameters. Whether $\beta$ is $0.9$ or $0.99$ makes a difference in effective decay length of the exponentially weighted sum. Do you have a number for $\omega$ or $\sigma^2_{\text{LR}}$? $\endgroup$– HansNov 24, 2017 at 22:05
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$\begingroup$ I do not. Sorry. $\endgroup$– Richard HardyNov 25, 2017 at 8:49
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Have found that using Alpha =0.06, Beta =0.93, omega =0.01 works fairly well. That is from calibrating to histories over quite long time periods.
