In the litterature the correlation between realized volatility of the stock and at the money implied volatility is often demonstrated.Some people said that the atm implied vol is the view of the expected future realized volatility. Is there a model which incorporate an EXPLICIT link between the realized and the implied volatility ?In the discrete framework it would be something likedS=r*S*dt+sigma(S,I)*S*N(0,1)*sqrt(dt) at the time n*dtwith I=atm implied vol at time (n-1)*dtIs there a study with a model similar to this ?

Heston-Nandi is a step in that direction, this is something that is worth looking at, as it improves on Dupire's Break even vol.

Thanks a lot MCarreira,I don't understand why the Heston Nandi is a step in that direction.Heston Nandi is a GARCH ancestor of Heston classical model with return givzen by a GARCH(1,1) stoch vol process if I remember well. I don't remember an explicit link in the model between implied vol and realized vol. Concerning the Dupire breakeven vol I have to reread this Bloomberg report as I don't remember enough to comment.

There's a feedback from realized vol into the process, which is something you want (clustering).

I agree that there is a feedback but it's a feedback from realized volatility to realized volatility. What I want is a feedback from implied volatility to realized volatility.Heston Nandi is Realized Vol at time t-1 into Realized Vol at time t while I want Implied Vol measure at time t-1 into Realized Vol at time t. It's also a kind of volatility clustering but a more complicated one that the classical serial autocorrelation described in the Heston Nandi GARCH process. My original idea came from a paper (highly controversial one it seems) whose the title is explicit : "Option Prices Leading Equity Prices: Do Option Traders Have an Information Advantage" I do not fully agree with them but it gave me the idea of this model.

Then make implied volatility react like the average volatility over time from the GARCH model, so large moves imply different moves on the term structure of implied vols.

I think I begin to see your point since in a 1 factor model there is a 1 to 1 correspondence between a local volatility function and the implied volatility function.

Longstaff might have done some work on this as well.

I think what you are looking for is a market model of implied volschoenbucher has done this... derman kani - discretelyas have carmona and ...?so you end up with no arbitrage conditions between implied vol and realised stock vol....I'd say its a bit of a dead end ... intractable... and better to look at bergomi's models

I'd look for some rules of thumb, not a full model.

I think you need to take into account the variance risk premium via the skew. Heuristically I believe that most variance swaps are priced off the the 90% put, not the ATM which implies that the expectations of realized variance/vol are not reflected in the ATM. I believe a variance swap is a purer (mathematically tractable) hedge against implied vol than a vol swap, the pricing allows for the bias. As per Longstaff, I have only read his very old work in which he relates the bias in the first moment of the implied risk neutral distribution from the option prices, i.e. Breeden Litzenberger. In his '95 paper he attributes the bias to frictions in the market place. But whether you are following Derman Kani, Carr Wu etc, the modeling for variance and vol swaps I think is fairly standard. As such, the weighting of the replicating portfolio uses the inverse of the strike squared biasing the overall towards the put skew implied vols. That's my interpretation but I am pretty sure it's close.

This paper explicitly talks about your concern:Expected Stock Returns and Variance Risk Premia (sorry, I cited the wrong paper)As far as a know, RV is a physical vol. IV is a risk-neutral vol. IV-RV measures something but it is still not clear. This recent paper also talks about it. http://papers.ssrn.com/sol3/papers.cfm? ... id=1538394