A Reduced-Form Model for Level-1 Limit Order Books
30 Pages Posted: 31 Aug 2015 Last revised: 20 Oct 2015
Date Written: August 29, 2015
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
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