There are many implied volatilities. Even if you are talking about an at-the-money implied volatility (IV), there is a different one for each option expiration.
If the option expiration is not tomorrow, then the IV will reflect events occurring beyond tomorrow. In addition, the farther away the expiration is, the more the IV will incorporate risk-aversion effects and be "too large" vs. the realized vols. (There is a very strong term structure effect). The good thing about IV's, however, is that they are *forward looking*.
ARCH/GARCH volatility estimates, on the other hand, are more time-uniform and reflect the actual stock price process without the strong risk-aversion effects. But they only know about history.
The bottom line is that tomorrow's volatility is quite hard to predict. Your best predictor will likely incorporate a combination of a GARCH-type model and the IV. Even then, it will only be mildly accurate.
edit: cross-posted with outrun, who already says a lot of what I say. But I will leave it with the following addition.
I make a point in a recent book that GARCH (alone) vol predictors are 'sub-optimal', as they do not account for forward-looking events.
Similarly, IV (alone) vol predictors will also be sub-optimal for the reasons given above + outrun's excellent reasons.
Last edited by Alan
on March 8th, 2018, 3:56 pm