INTRODUCTION

We will review the econometrics of nonparametric 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, modeling, 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 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 briefly discuss how econometricians have been attempting to overcome them.

In Section 2, we will set out the basis of the econometrics of arbitrage-free price processes, focusing on the centrality of quadratic variation. In Section 3, we will discuss central limit theorems for estimators of the QV process, while in Section 4, the role of jumps in QV will be highlighted, with bipower and multipower variation being used to identify them and to test the hypothesis that there are no jumps in the price process.