The Kyle (1985) model is extended to take into account market maker competition and the spread. It is shown that with a spread the Kyle model has a Nash equilibrium also with two market makers, not only with three or more, as shown in earlier research. The spread is endogenized, and two testable...

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, the Fourier estimator, and the wavelet estimator, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous...

This note clarifies the relation between two competing definitions of the contribution to pricediscovery in market microstructure models: (i) the information share and (ii) the common factorcomponent weight. It is demonstrated that the two measures are closely related, but that only...

We study the impact of the arrival of macroeconomic news on the informational and noise-driven components in high-frequency quote processes and their conditional variances. Bid and ask returns are decomposed into a common ('efficient return') factor and two market-side-specific components...

We find and describe four futures markets where the bid-ask spread is bid down to the fixed price tick size practically all the time, and which match counterparties using a pro-rata rule. These four markets' offered depths at the quotes on average exceed mean market order size by two orders of...

We model trades-through, i.e. transactions that reach at least the second level of limit orders in an order book. Using tick-by-tick data on Euronext-traded stocks, we show that a simple bivariate Hawkes process fits nicely our empirical observations of trades-through. We show that the...

This paper develops a market microstructure model with asymmetric information in order to quantify the influence which practical decision rules have on asset process. The users of practical decision rules have incomplete information at their disposal and trade in a market with both fully...