A Markov Model of a Limit Order Book: Thresholds, Recurrence, and Trading Strategies
Accepted version
Peer-reviewed
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Authors
Kelly, Frank https://orcid.org/0000-0002-7795-6049
Yudovina, E
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 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.
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Keywords
limit order book, queueing, fluid limit, high-frequency trading, Nash equilibrium
Journal Title
Mathematics of Operations Research
Conference Name
Journal ISSN
0364-765X
1526-5471
1526-5471
Volume Title
43
Publisher
Informs
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Sponsorship
The second author’s research was partially supported by the National Science Foundation [Grant DMS-1204311] and NSF Graduate Research Fellowship.