A Reduced-Form Model for Level-1 Limit Order Books

30 Pages Posted: 31 Aug 2015 Last revised: 20 Oct 2015

See all articles by Tzu-Wei Yang

Tzu-Wei Yang

University of Minnesota - Twin Cities - School of Mathematics

Lingjiong Zhu

University of Minnesota - Minneapolis

Date Written: August 29, 2015

Abstract

One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations. It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of the level-1 limit order books of a basket of stocks and study the numerical evidence of drift, correlation, volatility and their dependence on the imbalance. Based on the numerical discoveries, we develop a nonparametric discrete model for the dynamics of the best bid and ask, which can be approximated by a reduced-form model with analytical tractability that can fit the empirical data of correlation, volatilities and probability of price movement simultaneously.

Keywords: limit order books, data analysis, reduced form models, diffusion approximations

JEL Classification: C14, C32, C44, C51

Suggested Citation

Yang, Tzu-Wei and Zhu, Lingjiong, A Reduced-Form Model for Level-1 Limit Order Books (August 29, 2015). Available at SSRN: https://ssrn.com/abstract=2653149 or http://dx.doi.org/10.2139/ssrn.2653149

Tzu-Wei Yang (Contact Author)

University of Minnesota - Twin Cities - School of Mathematics ( email )

Minneapolis, MN 55455
United States

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

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