Equilibrium in a Dynamic Limit Order Market

Authors

  • RONALD L. GOETTLER,

  • CHRISTINE A. PARLOUR,

  • UDAY RAJAN

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    • Goettler and Parlour are at the David A. Tepper School of Business at Carnegie Mellon University. Rajan is at the Stephen M. Ross School of Business at the University of Michigan. The authors thank Dan Bernhardt, Hank Bessembinder, David Easley, Burton Hollifield, Mark Ready, Patrik Sandås, Duane Seppi, Joshua Slive, Chester Spatt, Peter Swan, Tom Tallarini, and seminar participants at the Bank of Canada, Carnegie Mellon, Houston, Michigan, NYU, North Carolina, Wisconsin, and the EFA (2003), IFM2 (Montréal), NBER Microstructure (2003), SITE (2003), and WFA (2004) meetings. We are especially grateful to Tony Smith for ideas generated in a project on simulating limit order books. The paper has benefitted from the comments of four anonymous referees and the editor, Rob Stambaugh.


ABSTRACT

We model a dynamic limit order market as a stochastic sequential game with rational traders. Since the model is analytically intractable, we provide an algorithm based on Pakes and McGuire (2001) to find a stationary Markov-perfect equilibrium. We then generate artificial time series and perform comparative dynamics. Conditional on a transaction, the midpoint of the quoted prices is not a good proxy for the true value. Further, transaction costs paid by market order submitters are negative on average, and negatively correlated with the effective spread. Reducing the tick size is not Pareto improving but increases total investor surplus.

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