  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.
