Optimal Placement in a Limit Order Book

26 Pages Posted: 1 Sep 2013 Last revised: 27 Jul 2016

See all articles by Xin Guo

Xin Guo

University of California, Berkeley

Adrien de Larrard

Université Paris VII Denis Diderot

Zhao Ruan

University of California, Berkeley

Date Written: July 25, 2016

Abstract

This paper proposes and studies an optimal placement problem in a limit order book. To gain some analytical insights, a simple correlated random walk model with mean-reversion is proposed for the best ask price. Optimal placement strategies for both single-period and multi-period cases are derived. In the single period model, the optimal strategy involves only the market order, the best bid, and the second best bid. In a multi-period model, the optimal strategy is a threshold type. The key component of the analysis for the two-dimensional optimization problem is a generalized reflection principle for the random walk.

In the appendix, a model with price impact is analyzed, to illustrate the connection between the optimal execution problem and the optimal placement problem.

Keywords: Optimal Placement, Optimal Execution, Limit Order Book, Correlated Random Walk, Price Impact

JEL Classification: C00, C60, C61, C69, N20

Suggested Citation

Guo, Xin and de Larrard, Adrien and Ruan, Zhao, Optimal Placement in a Limit Order Book (July 25, 2016). Available at SSRN: https://ssrn.com/abstract=2318220 or http://dx.doi.org/10.2139/ssrn.2318220

Xin Guo (Contact Author)

University of California, Berkeley ( email )

IEOR Department
4135 Etcheverry Hall
Berkeley, CA 94720
United States

HOME PAGE: http://www.ieor.berkeley.edu/~xinguo

Adrien De Larrard

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Zhao Ruan

University of California, Berkeley ( email )

IEOR Department
4135 Etcheverry Hall
Berkeley, CA 94720
United States

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