
Contents
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1 Introduction 1 Introduction
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1.1 Motivation 1.1 Motivation
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1.2 Background: The Continuous Double Auction 1.2 Background: The Continuous Double Auction
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1.3 The Model 1.3 The Model
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1.4 Summary of Prior Work 1.4 Summary of Prior Work
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2 Overview of Predictions of The Model 2 Overview of Predictions of The Model
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2.1 Dimensional Analysis 2.1 Dimensional Analysis
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2.2 Varying the Granularity Parameter Є 2.2 Varying the Granularity Parameter Є
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2.2.1 Depth Profile. 2.2.1 Depth Profile.
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2.2.2 Liquidity for Market Orders: The Price Impact Function. 2.2.2 Liquidity for Market Orders: The Price Impact Function.
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2.2.3 Spread. 2.2.3 Spread.
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2.2.4 Volatility and Price Diffusion. 2.2.4 Volatility and Price Diffusion.
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2.2.5 Liquidity for Limit Orders: Probability and Time to Fill. 2.2.5 Liquidity for Limit Orders: Probability and Time to Fill.
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2.3 Varying Tick Siz DP/PC 2.3 Varying Tick Siz DP/PC
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3 Summary of Analytic Results 3 Summary of Analytic Results
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3.1 Global Conservation Relations 3.1 Global Conservation Relations
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3.2 Order-Density Master Equation 3.2 Order-Density Master Equation
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3.3 Independent Interval Approximation 3.3 Independent Interval Approximation
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3.4 Utility of Analytic Results and Agreement with Simulation 3.4 Utility of Analytic Results and Agreement with Simulation
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4 Concluding Remarks 4 Concluding Remarks
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4.1 Ongoing Work on Empirical Validation 4.1 Ongoing Work on Empirical Validation
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4.2 Future Enhancements 4.2 Future Enhancements
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4.3 Comparison to Standard Models Based on Valuation and Information Arrival 4.3 Comparison to Standard Models Based on Valuation and Information Arrival
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Acknowledgments Acknowledgments
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References References
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A Random Order Placement Model of Price Formation in the Continuous Double Auction
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Published:October 2005
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Abstract
This chapter discusses the development of a model of a double auction trading mechanism in which “zero intelligence” agents interact in order to see what sorts of price and trading patterns emerge; interestingly, patterns appear to be empirically sensible. A microscopic dynamical statistical model is used for the continuous double auction under the assumption of IDD random order flow. The analysis is based on simulation, dimensional analysis, and theoretical tools based on mean-field approximations. The model makes testable predictions for all the basic properties of markets, including price volatility, the depth of stored supply and demand, the bid-ask spread, the price impact function, and the time and probability of filling orders. In most cases, the order size, which can be cast as a nondimensional granularity parameter, is a more significant determinant of market behavior than tick size.
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