Frank Kelly, joint work with
We describe our main result for the model, which is the existence of an explicit limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresholds. Fluid limits play an important role in establishing the recurrence properties of the model.
We use the model to analyze various high-frequency trading strategies (for example market-making, sniping and mixtures of these), and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.
Keywords: limit order book, queueing, fluid limit, high-frequency trading, Nash equilibrium
A Markov model of a limit order book: thresholds, recurrence, and trading strategies
Frank Kelly and Elena Yudovina
Mathematics of Operations Research, to appear