On the Correlation Structure of Microstructure Noise: A Financial Economic Approach

We introduce the financial economics of market microstructure into the financial econometrics of asset return volatility estimation. In particular, we use market microstructure theory to derive the cross-correlation function between latent returns and market microstructure noise, which feature prominently in the recent volatility literature. The cross-correlation at zero displacement is typically negative, and crosscorrelations at nonzero displacements are positive and decay geometrically. If market makers are sufficiently risk averse, however, the cross-correlation pattern is inverted. We derive model-based volatility estimators, which we apply to stock and oil prices. Our results are useful for assessing the validity of the frequently-assumed independence of latent price and microstructure noise, for explaining observed cross-correlation patterns, for predicting as-yet undiscovered patterns, and for microstructure-based volatility estimation. Acknowledgments: For comments and suggestions we thank Rob Engle, Peter Hansen, Charles Jones, Eugene Kandel, Gideon Saar, Frank Schorfheide, Enrique Sentana, and three anonymous referees. We are also grateful to participants at the NBER Conference on Market Microstructure, the Oxford-Man Institute Conference on the Financial Econometrics of Vast Data, and the Christmas Meeting of German Economists Abroad. We thank Ole E. Barndorff-Nielsen, Peter R. Hansen, Asger Lunde and Neil Shephard for sharing their data with us.