Academic literature on GARCH and flavors of GARCH runs in to tons of papers by various researchers. The idea behind GARCH and all its flavors is that there is a conditional variance equation governing the evolution of usual returns, the residuals of which were otherwise assumed homoscedastic. There are a lot of variations of this conditional variance equation which gives rise to various flavors of GARCH.

Some of the markets have seen EGARCH performing better than other flavors. In Indian markets though , some of the literature suggests that GARCH(1,1) outperforms ARCH and other flavors. Some researchers have also tried to improve GARCH(1,1) forecasts by incorporating Implied vol of the options as one of the predictors!!.However the data used in all these models is before the great crash in Indian markets where vix has seen crazy levels. Markets in 2008-2009 has seen Indian Market capitalization shrink from ~1T USD to 0.6T USD . A quick look at the Nifty log returns gives a good indication of the crazy vol levels that Indian markets is seeing. BTW, India VIX as of today is above 50. So, it was natural for me to think about Asymmetric GARCH in these markets and there might be a case for AGARCH models

**Nifty Log returns
**Image

Crunched some data on Symmetric and Asymmetric GARCH and found that it is indeed GJR GARCH, a version of asymmetric GARCH which has higher statistical power and forecasts better than Symmetric GARCH. Here is an illustration of the out of sample test results and the bands created by GJR GARCH do a good job of forecasting Vols(atleast a one month forecast seems ok)

GJR

I am running short of time on checking other fancy models..like arma+GJR GARCH, arma + T GARCH etc …But I would bet my money on Regime switching GARCH , considering that pre election & govt formation regime volatility would be very different from post government formation regime in India. It would be wise to take this effect in to consideration. It is very likely that Regime switching GARCH would capture the vol better than the current GJR GARCH that seems to be working well..Anyways , this forecast should be fine for now!

_Why should one care about a decent historical vol forecast at all ?
_Well, the reason being , if you want to know anything about Implied vol of NIFTY options, you got to get a hold on the underlying NIFTY volatility…Or else, “Omitted variable” bias will make your Implied vol model weak/useless :) ..

Aspects to think about : How to incorporate this historical vol in the implied vol model ? Should one just forget about historical vol and just fit a semi parametric model ? Hoping to get some clarity on these things in the days to come.