Can I use Implied volatility as a dependent variable in a GARCH model? I believe my IV data shows ARCH effects and hence can I use it to model volatility of the volatility? I know literature has used logged price differences in GARCH model, So I am a little confused If IV can be used or not (Since GARCH models historical volatility whereas IV is a forward looking measure)?
There is a famous paper by Day and Lewis (1992) which combines IV and GARCH-type models.
In this paper, the authors tested the information content of the IV from call options to GARCH and EGARCH models of conditional volatility by using the usual likelihood ratio test (i.e., LR=-2(Lr-Lu)). They added the IV to GARCH and EGARCH models as an explanatory variable. They found IV has significant explanatory power in in-sample analysis. However, they found mixed results for out-of-sample period.
Day and Lewis (1992). Stock market volatility and the information content of stock index options. Journal of Econometrics, 52, 267- 287. North-Holland.
Since IV is the market's forecast of the likely security price movements, yes you can use it as explanatory variable for change a security return.
I am asking about using it as a dependent variable not as an independent variable
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