Order Execution Probability and Order Queue in Limit Order Markets

The shaping of a limit order book illustrates the dynamics of the trading process, the changing pattern of the execution probability of limit orders therefore plays an important role. This paper presents a computable execution probability model for limit order market, as well as a numerical example that intuitively characterizes the changing pattern of the execution probability. The common effects of the lengths of both buy and sell queues on the execution probability are explored. In the limit book, the cumulative probability of limit orders is introduced as a crucial index of market depth to describe the shaping process which brings new insights into the structure of the order placement decision.