Order Execution Probability and Order Queue in Limit Order Markets
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Order Execution Probability and Order Queue in Limit Order Markets∗ ZHANG Qiang · WANG Chao · LIU Shancun · YANG Yaodong
DOI: 10.1007/s11424-020-9100-5 Received: 21 March 2019 / Revised: 2 September 2019 c The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2020 Abstract 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. Keywords Cumulative execution probability, execution probability, limit order, limit order book, market order.
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Introduction
In the limit order markets, traders exchange securities by submitting either a limit order or a market order. A limit order if executed, can offer the trader a better price than that of a market order, but there is an implied risk of losing the chance of execution. A market order transacts immediately at a price determined by the best quotes in the limit order book. Many theoretical models of optimal order submissions have been built based on the trade-offs between order prices, execution probability, and picking off risks. According to Cohen, et al.[1] , Harris[2] , ZHANG Qiang · WANG Chao School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China. LIU Shancun (Corresponding author) School of Economics and Management, Beihang University, Beijing 100191, China. Email: [email protected]. YANG Yaodong Unversity College London, Gower Street, London WC1E 6BT, UK. ∗ This research was supported by the National Natural Science Foundation of China under Grant Nos. 71371024 and 71771008, the Funds for the First-Class Discipline Construction under Grant No. XK1802-5, and the Fundamental Research Funds for the Central University under Grant Nos. PTRW1808 and YWF-19-BJ-W-45. This paper was recommended for publication by Editor WANG Shouyang.
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Parlour[3], Seppi[4] , Biais, et al.[5] , Foucault, et al.[6] , Goettler, et al.[7,8] , Zhang, et al.[9] and Cont[10,11] , market and limit order submitters consider the trade-offs. The choice between limit and market orders is important for most market participants. For instance, high-frequency traders can opportunistically provide liquidity with limit orders or consume it with market orders, a large group of mixed strategies actually rely on the demand schedule forming by both order types (Baron, et al.[12] , Brogaard, et al.[13] ). Numerous studies have focused on the dynamics of the limit order book, including Ranaldo[14
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