The dynamic evolution of limit order book driven by order flows
Guochao Jiang · JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING · 2011
The limit order book in continuous auction stock market could be viewed as a multi-server queueing system,where each price level was seen as a server.Then the limit order book could be modeled by a multi-dimensional random process.As order submission strategies of market participants often depended on the depth of limit order book,state-dependent Poisson processes were introduced to model the arrival and cancellation processes of limit order flows,namely the parameters of the Poisson processes depended on the state of limit order book.The dynamic evolution of limit order book driven by order flows was studied piecewise according to the moments of mid-price moves.The development of order quantity at each price level was proved to be a birth-death process before mid-price move.The transition probabilities and their Kolmogorov backward and forward differential equations of these birth-death processes were given.At the moment of mid-price move,the changes of bid/ask price and order quantity at each price level caused by different types of order submissions were analyzed.