Stylized facts of price gaps in limit order books: Evidence from Chinese stocks

TL;DR

This study analyzes the statistical properties of price gaps in Chinese stocks' limit order books, revealing power-law distributions, long-range correlations, multifractality, and buy-sell asymmetries, thus enhancing understanding of market liquidity dynamics.

Contribution

The paper provides the first detailed empirical analysis of price gap properties in Chinese stocks, uncovering their distribution, correlation, multifractality, and asymmetry, which were previously underexplored.

Findings

Price gaps follow a power-law distribution with an average tail exponent of 3.2.

Price gap time series exhibit long-range correlations and multifractal characteristics.

Buy-sell asymmetries are observed in the properties of price gaps.

Abstract

Price gap, defined as the logarithmic price difference between the first two occupied price levels on the same side of a limit order book (LOB), is a key determinant of market depth, which is one of the dimensions of liquidity. However, the properties of price gaps have not been thoroughly studied due to the less availability of ultrahigh frequency data. In the paper, we rebuild the LOB dynamics based on the order flow data of 26 A-share stocks traded on the Shenzhen Stock Exchange in 2003. Three key empirical statistical properties of price gaps are investigated. We find that the distribution of price gaps has a power-law tail for all stocks with an average tail exponent close to 3.2. Applying modern statistical methods, we confirm that the gap time series are long-range correlated and possess multifractal nature. These three features vary from stock to stock and are not universal. Furthermore, we also unveil buy-sell asymmetry phenomena in the properties of price gaps on the buy and sell sides of the LOBs for individual stocks. These findings deepen our understanding of the dynamics of liquidity of common stocks and can be used to calibrate agent-based computational financial models.