"Variation, jumps, market frictions and high frequency data in financial econometrics"

Ole E. Barndorff-Nielsen
Department of Mathematical Sciences,
University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark

and

Neil Shephard
Nuffield College, University of Oxford, Oxford OX1 1NF, UK

 

Abstract:     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.