1 When Is Noise Not Noise – A Microstructure Estimate of Realized

This paper studies the joint distribution of tick by tick returns and durations between trades. We build an econometric model for estimating and forecasting the volatility of stock returns using high-frequency data, correcting for the bias incurred by microstructure noise. Three features of the model are worth mentioning: first the conditional volatility adapts a structure which incorporates past days as well as recent trades’ information; second the volatility of returns is a nonlinear function of its contemporaneous duration; third the assumption of microstructure noise is general enough to encompass most of the properties implied from the theoretical literature. We apply the above model to frequently traded NYSE stock transactions data. It appears that contemporaneous duration has little effect on the volatility per trade after conditioning on the past, which means average per second volatility is inversely related to the duration between trades. Microstructure noise is found to be informative about the unobserved efficient price, and the informational component explains 45% of the total variation of the microstructure noise. * Previously titled “Forecasting Volatility Using Tick by Tick Data”. For comments and suggestions, we are greatly indebted to Joel Hasbrouk, Charles Jones, Lasse Pedersen, Gideon Sarr, Albert Menkveld and senimar participants at NBER microstructure group meeting, NYU Quantitative Financial Econometric meeting and European Financial Association annual conference at Moscow. 1 Department of Finance, Stern School of Business, New York University, [email protected]. 2 Department of Finance, Stern School of Business, New York University, [email protected].