The Mathematic Modeling Of Dynamic Limit Order Book

Nowadays,most of the stock exchanges are taking order-driven trading mechanism.It is different from traditional price-driven trading mechanism,in the order-driven market investors can hand in market order and limit order.These orders will make a bargain automatically using ‘priority of time,priority of price' principle.Those orders which are not traded will accumulate into limit order book.From the research we have already known and comparing with traditional market maker trading system,order-driven market is more effective functions searching for better prices and resources.Therefore,it is necessary to study the limit order book.The purpose of this paper is to try to construct a dynamic limit order book model based on Ising model and Bornholdt-Kaizoji-Fujiwara model.The existent models are mostly based on the assumptions that the investors are completely rational and chasing maximum utility.But the traditional assumptions appear to be limited with the development of financial research.For simulation of real stock trading mechanism,we simulate a artificial stock market based on continuous double auction transition trading mechanism using computational experiment financial method in MatlabR2011.In the simulation,we consider that specific investors could be influenced by two driving force.During the modeling process,we consider that the investors are influenced by two driving power.Partially speaking,they will be influenced by adjacent investors' conditions.Generally speaking,they will be influenced by most traders in the stock market.We mainly focus on the distribution of interest rate.The results of the simulation indicate us that the distribution of interest rate appears to be peak and thick tail compared with normal distribution.Afterwards,we try to fit the curve of the interest rate through student distribution.And we find that with the increasing of time interval ?,the freedom degree of fitted student distribution.Furthermore,we fit the distribution using more accurate function like power exponential function,it indicates that with the increase of time interval ?,the power exponential increases as well.And the positive and negative tail indices are close,within[3.5,4].After the simulation,we use the representative stock data from the stock market to do empirical research,the outcomes indicate that the actual indices of the positive and negative tail are a little bit bigger.But it is a classical standard fact that the interest rate's distribution has peak and fat tail.The innovation point of our paper is that we construct a limit order-driven book math model which can reflect the mechanism of limit order-driven book based on Ising model and Bornholdt-Kaizoji-Fujiwara model.The outcome is realized under comparably few parameters,so the model is clear,the programming process is brief and the simulation is accurate.The description about the model of our paper is different than other order-driven book model which only contain one variable because our model contains four aspects: the quoted price,the waiting time of order execution and trading price of investors.So our model is more abundant in describing dynamic order-driven mechanism in real stock market.