Quantifying bid-ask spreads in the Chinese stock market using limit-order book data: Intraday pattern, probability distribution, long memory, and multifractal nature

Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes (instead of the returns) possess multifractality. We find that the mass exponent $\tau(q)$ is linear and the singularity $\alpha(q)$ is close to 1 for all trading days and all indexes. Furthermore, we find strong evidence showing that the scaling behav...

We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets. We present a simple stochastic relation between the trading activity and return, which enables us to reproduce long-range memory statistical properties of volat...

In this paper, we investigate the cooling-off effect (opposite to the magnet effect) from two aspects. Firstly, from the viewpoint of dynamics, we study the existence of the cooling-off effect by following the dynamical evolution of some financial variables over a period of time before the stock price hits its limit. Secondly, from the probability perspective, we investigate, with the logit model, the existence of the cooling-off effect through analyzing the high-frequency da...

Properties of distributions of the number of trades in different intraday time intervals for five stocks traded in MICEX are studied. The dependence of the mean number of trades on the capital turnover is analyzed. Correlation analysis using factorial and $H_q$ moments demonstrates the multifractal nature of these distributions as well as some peculiar changes in the correlation pattern. Guided by the analogy with the analysis of particle multiplicity distributions in multipa...

Long-range correlation in financial time series reflects the complex dynamics of the stock markets driven by algorithms and human decisions. Our analysis exploits ultra-high frequency order book data from NASDAQ Nordic over a period of three years to numerically estimate the power-law scaling exponents using detrended fluctuation analysis (DFA). We address inter-event durations (order to order, trade to trade, cancel to cancel) as well as cross-event durations (time from orde...

In order-driven markets, limit-order book (LOB) resiliency is an important microscopic indicator of market quality when the order book is hit by a liquidity shock and plays an essential role in the design of optimal submission strategies of large orders. However, the evolutionary behavior of LOB resilience around liquidity shocks is not well understood empirically. Using order flow data sets of Chinese stocks, we quantify and compare the LOB dynamics characterized by the bid-...

We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time of a limit order as a function of the distance from the best price. We also determine the `price impact' function using French and British stocks, and find a logarithmic, rather than a power-law, dependence of the price response on the vol...

We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price according to a power-law, and it isn't randomly drawn from the distribution, but has a strong correlation with the size of cumulative unexecuted limit orders on th...

Taylor's law of temporal fluctuation scaling, variance $\sim$ $a($mean$)^b$, is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity of almost all stocks traded on the Shanghai Stock Exchange (SHSE) and the Shenzhen Stock Exchange (SZSE) during the period from 1999 to 2011. Taylor's law holds ...

We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold $q$ are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the...