Physics of Society: Econophysics and Sociophysics. Limit Order Books

Transcription

1 Physics of Society: Econophysics and Sociophysics Limit Order Books Frederic Abergel Marouane Anane Anirban Chakraborti Aymen Jedidi Ioane Muni Toke CAMBRIDGE UNIVERSITY PRESS

2 Contents Figures Tables Foreword Preface Acknowledgments xi XV xvii xix xxi 1 Introduction 1 PART ONE EMPIRICAL PROPERTIES OF ORDER-DRIVEN MARKETS 2 Statistical Properties of Limit Order Books: A Survey Introduction Time of Arrivals of Orders Volume of Orders Placement of Orders Cancellation of Orders Average Shape of the Order Book Intraday Seasonality Conclusion 19 3 The Order Book Shape as a Function of the Order Size Introduction Methodology The Regression Model Conclusion 28 4 Empirical Evidence of Market Making and Taking Introduction Re-introducing Physical Time Dependency Properties of Inter-anival Times 31

3 viii Empirical evidence of market making A reciprocal effect? Further Insight into the Dependency Structure The fine structure of inter-event durations: Using lagged correlation matrices Conclusion 41 PART TWO MATHEMATICAL MODELLING OF LIMIT ORDER BOOKS 5 Agent-based Modelling of Limit Order Books: A Survey Introduction Early Order-driven Market Modelling: Market Microstructure and Policy Issues A pioneer order book model Microstructure of the double auction Zero-intelligence Order-driven Market Modelling in Econophysics The order book as a reaction-diffusion model Introducing market orders The order book as a deposition-evaporation process Empirical Zero-intelligence Models Some Analytical and Mathematical Developments in Zero-intelligence Order Book Modelling Conclusion 58 6 The Mathematical Structure of Zero-intelligence Models Introduction An elementary approximation: Perfect market making Order Book Dynamics Model setup: Poissonian arrivals, reference frame and boundary conditions Evolution of the order book Infinitesimal generator Price dynamics Ergodicity and Diffusive Limit Ergodicity of the order book Large-scale limit of the price process 70

4 ix Interpreting the asymptotic volatility The Role of Cancellations Conclusion " 76 7 The Order Book as a Queueing System Introduction A Link Between the Flows of Orders and the Shape of an Order Book The basic one-sided queueing system A continuous extension of the basic model Comparison to Existing Results on the Shape of the Order Book Numerically simulated shape in Smith et al. (2003) Empirical and analytical shape in Bouchaud et al. (2002) A Model with Varying Sizes of Limit Orders Inftuence of the Size of Limit Orders on the Shape of the Order Book Conclusion 96 8 Advanced Modelling of Limit Order Books Introduction Towards Non-trivial Behaviours: Modelling Market Interactions Herding behaviour Fundamentalists and trend followers Threshold behaviour Enhancing zero-intelligence models Limit Order Book Driven by Hawkes Processes Hawkes processes Model setup The infinitesimal generator Stability of the order book Large scale limit of the price process Conclusion 110 PARTTHREE SIMULATION OF LIMIT ORDER BOOKS 9 Numerical Simulation of Limit Order Books Introduction Zero-intelligence Limit Order Book Simulator An algorithm for Poissonian order flows Parameter estimation 115

5 X Performances of the Simulation Anomalous diffusion at short time scales Results for CAC 40 stocks Simulation of a Limit Order Book Modelled by Hawkes Processes Simulation of the limit order book in a simple Hawkes model Algorithm for the Simulation of a Hawkes process Parameter estimation Performances of the Simulation Market Making and Taking, Viewed from a Hawkes-process Perspective Conclusion 141 PART FOUR IMPERFECTION AND PREDICTABILITY IN ORDER-DRIVEN MARKETS 10 Market Imperfection and Predictability Introduction Objectives, Methodology and Performances Measures Objectives Methodology Performance measures Conditional Probability Matrices Binary case Four-class case Linear Regression Ordinary least squares (OLS) Ridge regression Least Absolute Shrinkage and Selection Operator (LASSO) Elastic net (EN) Conclusion 167 Appendix A A Catalogue of Order Types 169 Appendix B Limit Order Book Data 171 AppendixC Some Useful Mathematical Notions 176 Appendix D Comparison of Various Prediction Methods 187 Bibliography 209