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

This paper studies the joint distribution of tick by tick returns and durations between trades. Returns are decomposed into changes in full information prices and microstructure noise, but the noise is modeled in accordance with various models of market microstructure allowing rich correlation structures both with the efficient price and over time. The full information price has time varying volatility which depends upon the arrival time of trades. The paper aims at three contributions: First, the noise is modeled to allow asymmetric information, inventory and order processing costs, and delayed quote setting. Second, the response to the trade arrival times allows trade durations to be informative on future volatility. Third, the estimated state space models can act as a laboratory to examine various non-parametric approaches to realized volatility estimation. Both simulated and actual data can be compared across methods and the accuracy and efficiency assessed as long as the parameteric model is viewed as a sufficiently accurate representation. We apply the above model to 10 NYSE stock transactions data series with varying transaction rates. 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