Markovian Order Book Modeling

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Table of contents

Contents
Introduction
Motivations
Outline
1 Part I: Limit Order Book Modeling
1.1 The Queue-reactive Model
1.2 A General Framework for Markovian Order Book Modeling
2 Part II: Tick Value Eects
2.1 The Eects of Tick Value Changes on Market Microstructure: Analysis of the 2014 Japanese Experiment
2.2 An Agent-based Model on Order Book Dynamics
Part I Limit Order Book Modelling
I The queue-reactive model
1 Introduction
2 Dynamics of the LOB in a period of constant reference price
2.1 General Framework
2.2 Data description and estimation of the reference price
2.3 Model I: Collection of independent queues
2.4 Model II: Dependent case
2.5 Example of application: Probability of execution
3 The queue-reactive model: a time consistent model with stochastic LOB and dynamic reference price
3.1 Model III: The queue-reactive model
3.2 Example of application: Order placement analysis
4 Conclusion and perspectives
5 Appendix
5.1 Proof of Theorem 1
5.2 Computation of condence intervals
5.3 Quasi birth and death process
5.4 Order Placement Tactic Analysis
5.5 Alcatel-Lucent
5.6 AES
II A General Framework for Markovian Order Book Models
1 Introduction
2 A general Markovian framework
2.1 Representation of the order book
2.2 Dynamics of the order book
2.3 Comparison with existing models
3 Ergodicity
3.1 When pr e f stays constant
3.2 General case
4 Scaling limits
5 Some specic models
5.1 Best bid/best ask Poisson model (Cont and De Larrard (2013))
5.2 Poisson model with K È 1
5.3 Zero-intelligence model
5.4 Queue-reactive model (Huang, Lehalle, and Rosenbaum (2013))
6 Conclusion
7 Appendix
7.1 Proof of Theorem 1
7.2 Proof of Theorem 2
7.3 Proof of Theorem 3
7.4 Proof of Theorem 5
Part II Tick Size Eects
III The Eect of Tick Value Changes on Market Microstructure: Analysis of the Japanese Experiements 2014
1 Introduction
2 Cost of trading and high frequency price dynamics
2.1 The model with uncertainty zones: When the tick prevents price discovery
2.2 Perceived tick size and cost of market orders
2.3 Implicit bid-ask spread and cost of limit orders
2.4 Prediction of the cost of market and limit orders
2.5 What is a suitable tick value?
3 Analysis of the Tokyo Stock Exchange pilot program on tick values
3.1 Data description
3.2 Classication of the stocks in Phase 0
3.3 Phase 0 – Phase 1
3.4 Phase 1 – Phase 2
4 Conclusion
IV Intelligence and Randomness of Market Participants
1 Introduction
2 Basic Model
2.1 Price Dynamics
2.2 Informed Trader, Noise Trader and Market Maker
2.3 Some Assumptions
2.4 Links between the Trade Size Q, Price Jump B and the LOB Cumulative Shape L(x)
2.5 The Bid-Ask Spread and the Equilibrium LOB Shape
2.6 Variance per Trade
3 Tick Size
3.1 Constrained Bid-Ask Spread
3.2 Daily Volume
3.3 Priority Value
4 Examples
4.1 Power-law Distributed Information
5 Generalization
5.1 How Information is Digested
6 Conclusion and perspectives
Bibliography