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Unformatted text preview: (In)Stability Properties of Limit Order Dynamics Eyal Even-Dar * Sham M. Kakade Michael Kearns Yishay Mansour Abstract We study the stability properties of the dynamics of the standard continuous limit-order mechanism that is used in modern equity markets. We ask whether such mechanisms are susceptible to butterfly effects the infliction of large changes on common measures of market activity by only small perturbations of the order sequence. We show that the answer depends strongly on whether the market consists of absolute traders (who determine their prices independent of the current order book state) or relative traders (who determine their prices relative to the current bid and ask). We prove that while the absolute model enjoys provably strong stability properties, the relative model is vulnerable to great instability. Our theoretical results are supported by large-scale experiments using limit order data from INET, a large electronic exchange for NASDAQ stocks. 1. INTRODUCTION In recent years there has been an explosive increase in the automation of modern equity markets. This increase has taken place both in the exchanges, which are increas- ingly computerized and offer sophisticated interfaces for or- der placement and management, and in the trading activity itself, which is ever more frequently undertaken by software. The so-called Electronic Crossing Networks (or ECNs) that dominate trading in NASDAQ stocks are a common exam- ple of the automation of the exchanges. On the trading side, computer programs now are entrusted not only with * Department of Computer and Information Science, Univer- sity of Pennsylvania, Philadelphia PA. Email address: even- firstname.lastname@example.org Toyota Technological Institute, Chicago IL. Email address: email@example.com Department of Computer and Information Science, Uni- versity of Pennsylvania, Philadelphia PA. Email address: firstname.lastname@example.org School of Computer Science, Tel Aviv University, Tel Aviv, Israel. Email address: email@example.com Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Copyright 200X ACM X-XXXXX-XX-X/XX/XX ... $ 5.00. the careful execution of large block trades for clients (some- times referred to on Wall Street as program trading), but with the autonomous selection of stocks, direction (long or short) and volumes to trade for profit (commonly referred to as statistical arbitrage)....
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This note was uploaded on 12/08/2011 for the course CIS 625 taught by Professor Michaelkearns during the Spring '12 term at Pennsylvania State University, University Park.
- Spring '12