Estimating Co variation: Epps Effect, Microstructure Noise

Lan ZhangLan Zhang

Bio sketch:
Lan Zhang is Reader in Finance at the Saïd Business School. Her research focuses on market microstructure, statistical arbitrage, and high frequency financial econometrics.
Lan Zhang has published in leading journals including Econometrica, Review of Financial Studies, Journal of Econometrics, Journal of American Statistical Association, Bernoulli, and Annals of Statistics. She is an associate editor for the academic journal Statistics and Its Interface. She sits on the advisory board of the International Centre for Futures and Derivatives at the University of Illinois at Chicago. She is Senior Research Fellow at the Oxford-Man Institute of Quantitative Finance.
Before joining Oxford, she was an Associate Professor at the University of Illinois at Chicago and an Assistant Professor at the Carnegie Mellon University (2001-2005). She was an undergraduate at Peking University and obtained her master’s and PhD degree from the University of Chicago. She spent 2000-2001 at Princeton University as Exchange Scholar.
Abstract:
This paper is about how to estimate the integrated covariance of two assets over a fixed time horizon [0, T], when the observations of X and Y are “contaminated” and when such noisy observations are at discrete, but not synchronized, times. We show that the usual previous-tick covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. This is an analytic characterization of the Epps effect. We also provide optimal sampling frequency which balances the trade-off between the bias and various sources of stochastic error terms, including non synchronous trading, microstructure noise, and time discretization. Finally, a two-scale covariance estimator is provided which simultaneously cancels (to first order) the Epps effect and the effect of microstructure noise. The gain is demonstrated in data.

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