Hydrodynamic limit of order book dynamics

In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a certain sense. We also test our fluid approximation on data. The empirical results suggest that the approximation is reasonably good for liquidly--traded stocks in certain time periods

A Challenger to the Limit Order Book: The NYSE Specialist

This paper gives a new answer to the challenging question raised by Glosten (1994): "Is the electronic order book inevitable?". While the order book enables traders to compete to supply anonymous liquidity, the specialist system enables one to reap the benefits from repeated interaction. We compare a competitive limit order book and a limit order book with a specialist, like the NYSE. Thanks to non-anonymous interaction, mediated by brokers, uninformed investors can obtain good liquidity from the specialist. This, however, creates an adverse selection problem on the limit order book. Market liquidity and social welfare are improved by the specialist if adverse selection is severe and if brokers have long horizon, so that reputation becomes a matter of concern for them. In contrast, if asymmetric information is limited, spreads are wider and utilitarian welfare is lower when the specialist competes with the limit order book than in a pure limit order book market.Limit order book; specialist; hybrid market

Designating market maker behaviour in Limit Order Book markets

Financial exchanges provide incentives for limit order book (LOB) liquidity provision to certain market participants, termed designated market makers or designated sponsors. While quoting requirements typically enforce the activity of these participants for a certain portion of the day, we argue that liquidity demand throughout the trading day is far from uniformly distributed, and thus this liquidity provision may not be calibrated to the demand. We propose that quoting obligations also include requirements about the speed of liquidity replenishment, and we recommend use of the Threshold Exceedance Duration (TED) for this purpose. We present a comprehensive regression modelling approach using GLM and GAMLSS models to relate the TED to the state of the LOB and identify the regression structures that are best suited to modelling the TED. Such an approach can be used by exchanges to set target levels of liquidity replenishment for designated market makers

Limit order book as a market for liquidity

We develop a dynamic model of an order-driven market populated by discretionary liquidity traders. These traders must trade, yet can choose the type of order and are fully strategic in their decision. Traders differ by their impatience: less patient traders demand liquidity, more patient traders provide it. Three equilibrium types are obtained - the type is determined by three parameters: the degree of impatience of the patient traders, which we interpret as the cost of execution delay in providing liquidity; their proportion in the population, which is the cost of the minimal price improvement. Despite its simplicity, the model generates a rich set empirical predictions on the relation between market parameters, time to execution, and spreads. We argue that the economic intuition of this model is robust, thus its main results will remain in more general models.limit and market orders; time-to-execution; market quality