We will review the econometrics of non-parametric estimation of the components of the variation of asset prices. This very active literature has been stimulated by the recent advent of complete records of transaction prices, quote data and order books. In our view the interaction of the new data sources with new econometric methodology is leading to a paradigm shift in one of the most important areas in econometrics: volatility measurement, modelling and forecasting. We will describe this new paradigm which draws together econometrics with arbitrage free financial economics theory. Perhaps the two most influential papers in this area have been Andersen, Bollerslev, Diebold and Labys(2001) and Barndorff-Nielsen and Shephard(2002), but many other papers have made important contributions. This work is likely to have deep impacts on the econometrics of asset allocation and risk management. One of our observations will be that inferences based on these methods, computed from observed market prices and so under the physical measure, are also valid as inferences under all equivalent measures. This puts this subject also at the heart of the econometrics of derivative pricing. One of the most challenging problems in this context is dealing with various forms of market frictions, which obscure the efficient price from the econometrician. Here we will characterise four types of statistical models of frictions and discuss how econometricians have been attempting to overcome them.
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