A Relation between the Efficient, Transaction and Mid Prices : Disentangling Sources of High Frequency Market Microstructure Noise

We consider an extension of the Roll model where the trade direction, i.e. whether the trade is buyer or seller initiated, is multiplied by the dynamic quoted half-spread. Employing tick-by-tick maximum likelihood estimation on S&P 500 constituents, we find that the efficient price is quite close yet not equal to the mid price and lies systematically on the side of the trade, suggesting that there is additional information in trade direction. Moreover, we document that the variability in the model is relatively small, indicating that the combination of the trade direction and quoted bid-ask spread plays the major role in explaining market microstructure noise. Among different observable high frequency financial characteristics of the underlying stocks, this variability is best explained by the tick-to-spread ratio, implying that discreteness is the second source of noise. We determine the bid-ask bounce effect as the third source of noise