Hydrodynamic Limit of Order Book Dynamics

51 Pages Posted: 28 Nov 2014

See all articles by Xuefeng Gao

Xuefeng Gao

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

J. Dai

Operations Research & Information Engineering

Ton Dieker

Columbia University - Fu Foundation School of Engineering and Applied Science

Shijie Deng

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Date Written: November 20, 2014

Abstract

Motivated by optimal trade execution, this paper studies the temporal evolution of the shape of a limit order book over a time horizon that is large compared with the length of time between order book events, with the aim of approximating the transient distribution of the shape. Relying on the stochastic order book model in Cont et al. (2010), we show that when the tick size approaches zero, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a certain sense. Moreover, we describe the density profile of the limiting processes through ordinary differential equations which can be solved explicitly. We also perform experiments to test our limiting model against data. The empirical results suggest that the approximation is effective.

Keywords: limit order book, fluid approximation, scaling limit, optimal execution, measure-valued processes

Suggested Citation

Gao, Xuefeng and Dai, J. and Dieker, Ton and Deng, Shijie, Hydrodynamic Limit of Order Book Dynamics (November 20, 2014). Available at SSRN: https://ssrn.com/abstract=2530306 or http://dx.doi.org/10.2139/ssrn.2530306

Xuefeng Gao (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong

J. Dai

Operations Research & Information Engineering ( email )

226 Rhodes Hall
136 Hoy Road
Ithaca, NY 14853
United States

Ton Dieker

Columbia University - Fu Foundation School of Engineering and Applied Science ( email )

New York, NY
United States

Shijie Deng

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

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