A Markov model of a limit order book: thresholds, recurrence, and trading strategies

TL;DR

This paper presents a stochastic Markov model of a limit order book, analyzing its long-term behavior, thresholds, and trading strategies, with implications for high-frequency trading and market design.

Contribution

It introduces a tractable Markov model for limit order books, establishing distribution thresholds, recurrence properties, and analyzing high-frequency trading strategies and equilibria.

Findings

Existence of limiting distributions confined between thresholds.

Recurrence properties of the order book dynamics.

Insights into Nash equilibria among high-frequency traders.

Abstract

We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand. We establish the existence of a limiting distribution for the highest bid, and for the lowest ask, where the limiting distributions are confined between two thresholds. We make extensive use of fluid limits in order to establish recurrence properties of the model. We use the model to analyze various high-frequency trading strategies, and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.