High-frequency Analysis Of The Transaction Probability And Microstructure Of Limit Orders In The Chinese Stock Market

With the rapid development of programmatic high-frequency trading in China's financial market,high-frequency analysis of the market microstructure of the Chinese stock market has become increasingly urgent.70% of trading in the US market are completed by algorithms and high-frequency trading,while the current algorithmic and high-frequency trading in the Chinese market account for only about 10%.With the gradual opening of financial markets,the volume of algorithms and high-frequency trading will increase rapidly.One of the characteristics of high-frequency trading is that the trading fee accounts for a high proportion,often exceeding 50%,so using limit orders instead of market orders is one way to offset transaction costs.The second characteristic of high-frequency trading is frequent offering and cancelling orders.For some high-frequency trading strategies,such as market-making strategies,flexible switching between limit orders and market orders is required.In recent years,largevolume trading also need to use algorithmic trading strategies such as TWAP and WWAP to reduce market impact costs.The core is also to replace market orders with limit orders as much as possible.So it is very important to study the trading probabilities of limit orders.In recent years,the main research area for high-frequency trading in China and abroad is the dynamic changes of order book(LOB).The order book has many dimensions and large state space,which are difficult to model and describe with accurate mathematical models.Scholars have constructed stochastic processes,statistical methods,or deep learning models to study the formation and evolution of prices and volatility.However,the modeling of dynamic processes still uses a lot of static variables,which makes the characterization of order book dynamic not accurate enough.This article analyzes the dynamic process of the order book by modeling the Level-2 snapshot tick,order by order and trade by trade data of the Shenzhen Stock Exchange,and dynamically calculates order book through the multi-dimensional hawkes model and order book millisecond high-frequency reconstruction,based on the distribution of real transaction time,the imbalance of order rates,and the linear model estimated the trading probabilities of limit orders.Through analysis of the model parameters and trading probabilities,the microstructure characteristics of the Chinese stock market under high frequency were found.This paper first studies and analyzes the trading mechanism and order book characteristics of the Chinese stock market.Explains the entire process of participants in the Chinese stock market from the client's orders to the order book queue of the exchange,and the completion of the transaction.The main technology of highfrequency trading,the programmatic transaction process,and the impact of network delay on the trading,the main principles of high-frequency strategies.Use mathematical definitions to describe the formation mechanism of order books and the generation of order books is the result of continuous bilateral auctions.It explains the mutual constraints between various events in order books.The order flow,price and transaction volume need to meet the principle of consistency.Further show that price is an endogenous variable of order book dynamics.The arrival rate,order price,timing,and order size of the limit order and market order in the order book determine the market price.The interactions between them determine the form of the order book at all times,which is also the theoretical basis for the high-frequency reconstruction of the order book in this article.Through the study of order flow,it is found that the microstructure of the Chinese and American stock markets is different.The order flow in the order book of the Chinese stock market has been in an imbalance state for a long time,with an average imbalance ratio of 35%.Due to the restrictions on frequent cancellation of orders in the Chinese market,the average cancellation rate is 8%,while the US market is about 35%.Due to the restrictions on frequent cancellation of orders in the Chinese market,the average cancellation rate is 8%,while the US market is about 35%.Therefore,the imbalance of order flow(OFI)in the Chinese stock market cannot explain the short-term price trend.This article introduces the imbalance of the efficiency of the execution of limit orders per unit time in the buy / sell queue through the time dimension of the order.Indicator,the OEI of the order book is found to be an important factor affecting the high-frequency changes in prices through the linear model.When OEI is added into the Cont and Kukanov(2013)model to explain the price change,its R-squared is higher than the previous model in the Chinese market 47.8%,36.8%,and 45.9%.When market liquidity is more abundant,OEI's explanatory power increases by 477.2%,387.6%,and 333.9% compared to when liquidity is normal.This paper continues to study the dynamic characteristics of the order book through the time dimension,and calculates the rate of order arrival in the queue and the trading probabilities of limit orders.And then the paper shows that the impact of order arrival on the order book is continuously changing,and the effect is diminishing with time,so the multidimensional hawkes model with a negative exponential kernel function is used to describe the interaction between orders.Based on the multi-dimensional hawkes process,the paper establishes a model for the interaction between order arrival rates,and uses the interior point method to solve its maximum likelihood function.Finally,based on nonlinear optimization,the parameter values are used to dynamically calculate the instantaneous rate of bid decrease,bid-increase,ask decrease and ask increase at which each order reaches the order book queue for each of the four types of orders.Each order rate is affected by the arrivals of other types of orders.The time complexity of the multidimensional hawkes model is analyzed,and the time complexity of modeling and solving with high-frequency data(accurate to milliseconds)is very high.Mathematically speaking,it is a computationally intensive problem.The article completely changed the previous static method of studying the order rate as a "uniform linear motion" over a period of time.By analyzing the parameters of the multidimensional hawkes model,it is found that the relative size of the jump amplitude in the parameter is consistent with the rapid changes of the best buy / sell price in the same high-frequency time period;the relative size of the decay rate in the parameters are consistent with length varies of best buy / sell queue.It is an important discovery in the high-frequency field of China's stock market microstructure.At the same time,in order to provide another order rate fast computation and calculate the trading probabilities of limit orders.The fifth chapter establishes a realtime order book high-frequency reconstruction algorithm to dynamically describe the shape of the order book at every moment through the order by order and trade by trade data,so that the order book refresh frequency is upgraded from 3 seconds to 10 ms or update the order book once an order book event occurs.Thus,changes the computation of order rate from hawkes model to directly addition and subtraction operations on the order book queue.The high-frequency reconstruction of the order book brings three major effects:(1)It can determine 100% accurately when an order book event occurs,on which queue of the order book,and which price position,so as to determine whether it belongs to the best bid or ask queue;(2)dynamically calculates the change in the rate of each order,instead of the average value in a time period;(3)in addition to multidimensional hawkes model with high time complexity,it provides an ordinary servers can calculate order rate in real-time to ensure the timeliness of trading signals.Chapter 6 first analyzes the distribution of the transaction time of limit orders,and finds that as the transaction time increases,the number of limit orders gradually becomes sparse and steep,and the buy / sell distribution is basically symmetrical.Based on historical data,the actual trading probabilities of the limit orders are calculated under the condition that the middle price is unchanged.It is found that the actual trading probabilities of all experimental target stocks increases rapidly and then decreases slowly with the length of the trading time.The trend of the ratio of the consumption rate to the order depth is completely consistent with actual trading probabilities.The above rule has become an important basis for calculating the real-time probability of a limit order based on a linear model.Based on the order rate obtained from the multidimensional hawkes model and high-frequency reconstruction of the order book,an estimate of the trading probability of the limit order was performed: First,the first passage time and the diffusion limit method were used to calculate the trading probability of the limit order under the order rate balance.It is found that it is far from the actual probability distribution,and the shortcomings of this method are analyzed.However,it was found that the volatility was negatively correlated with the trading time of the limit order.Secondly,under the condition that the order rate is imbalanced at most time,the time required to trade a limit order is estimated by the order rate and the linear equation,and the required time is used to find the trading period that has been in the past historical limit order actual trading,compared with time-probability table,this probability is the real-time trading probability estimated by this linear model.Thus,the conversion from the trading time of the limit order to the trading probability is completed.Thereby,according to the change of the actual trading time distribution of the latest limit orders,the model can more accurately estimate the trading probability of the limit order.In the sample,it is found that the accuracy of the probability estimation of some stocks in consecutive months is very high,the estimated accuracy can reach 80% at the highest,and in the same time period,the actual probability and the model calculated probability trend are consistent.Outside the sample,the accuracy is lower than inside the sample,but it is still higher.The actual probability is sometimes consistent with the model's calculated probability trend,and sometimes it changes.By comparison,it is found that the average accuracy rate of limit order transaction probability calculated based on the multi-dimensional hawkes model is higher than that based on the order book high frequency reconstruction method.Finally,it is found that based on the average value of the multi-dimensional hawks parameters of the stock throughout the trading day,it is found that the microstructure of the Chinese stock market at high frequency scale has three major characteristics:(1)The consumption rate of the order book queue is almost greater than the growth rate of the queue.(2)Price changes are mainly caused by the impact of market orders(active orders).The impact of market orders comes quickly and goes quickly;while limit orders come slowly,but the effect lasts a long time.Increasing of queue length is a relatively continuous slow process.(3)There is a clear promotion effect between different order types,and its effect is even greater than the self-exciting effect of the order itself.Based on the research of paper,total 9 high frequency features are explored and summarized in the area of Chinese stock market microstructure.Finally,for the intraday mode,the total jump amplitude difference in the buy and sell direction is calculated and the direction of difference is consistent with the direction of difference between the intraday closing price and the opening price.The research can provide methodological support for high frequency trading,especially for market making strategies and VWAP or TWAP.It is significance to improve the research of market microstructure of Chinese stock market especially on high frequency observations.