The risk-return trade-off being the very substance of finance, volatility has always been an essential parameter for portfolio management. Moreover, the generalization of the use of derivatives has placed in the forefront the concept of volatility risk: i.e. the model risk generated by treating the volatility as a constant parameter, when it is in fact volatile. Hence the econometrician is asked for accurate measures and reliable forecasts of volatility, not only for pricing and hedging derivatives, but also more generally for portfolio management. The central thesis of this paper is that operational model-free methods of volatility forecasting do not exist any more than do arbitrage opportunities (free lunches) in financial markets. It is for this reason that there exists volatility model risk against which it is illusory to try to immunize. Several specific components of this model risk are analyzed. One will imply that the choice of a volatility model for a given financial application always confronts one with a risk-return trade-off on the model itself.