Econophysics of Order-driven Markets

Name: Econophysics of Order-driven Markets
Brand: Springer
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Frédéric Abergel Bikas K. Chakrabarti Anirban Chakraborti Manipushpak Mitra(Editor)

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1st Edition

Published on 6. April 2011

XV, 309 pages

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Content

Intro
Title Page
Copyright Page
Preface
Table of Contents
List of Contributors
Part I Order Book Data and Modelling
Trade-throughs: Empirical Facts and Application to Lead-lag Measures
1 Introduction
2 Data Presentation
2.1 General TRTH Data Presentation and BNP-Paribas's Processing
2.2 Data Used in This Study
3 Some Statistics on Trade-throughs
3.1 Definition of Trade-throughs
3.2 Basic Statistics on Occurrences and Volumes of Trade-throughs
3.3 Stability of Trade-through's Definition with the Size of the Trade
3.4 Intraday Timestamp Distribution of Trade-throughs
4 Spread Relaxation
5 Lead-lag Parameter Estimation from Trade-throughs Time-Series
5.1 Using Trade-throughs to Measure Empirical Distribution of Lead-lag Parameter
5.2 Empirical Measure of Lead-lag Parameter
5.2.1 Lead-lag Parameter: the Estimation Technique
5.3 Empirical Results for the Lead-lag Between US and EU Equity Markets
6 Conclusions
References
Are the Trading Volume and the Number of Trades Distributions Universal?
1 Introduction
2 The Indian Financial Market
3 Results
4 Conclusions
References
Subpenny Trading in US Equity Markets
1 Equity Market Structure - Introduction
1.1 SEC Concept Release
1.2 Minimum Price Variation
1.3 Two Different Points of View
1.3.1 Broker-dealers
1.3.2 High Frequency Traders
2 Empirical Study
2.1 Methodology and Data
2.2 Results
2.2.1 Price Improvement Distribution
2.2.2 Correlation with the Stock's Price
2.2.3 On the Importance of Queue Jumping
2.2.4 Sub-penny Trading Provides Price Improvement
2.3 Historical Evolution
2.3.1 Evolution of the Importance of Sub-penny Trading
2.3.2 Evolution of the Price Improvement Distribution
3 Discussion
3.1 Minimum Price Variation
3.2 Sub-penny for Everyone
3.3 Banning Queue Jumping
4 Conclusions
References
"Market Making" in an Order Book Model and Its Impact on the Spread
1 Introduction
Arrival Times of Orders: Event Time Is Not Enough
Counting Processes with Dynamic Intensity
Organization of This Paper
2 Empirical Evidence of "Market Making"
2.1 Data and Observation Setup
2.2 Empirical Evidence of "Market Making"
2.3 A Reciprocal "Market Following Limit" Effect?
3 Order Book Models with Mutually Exciting Order Flows
3.1 The Basic Poisson Model
3.2 Adding Dependence Between Order Flows
4 Numerical Results on the Order Book
4.1 Fitting and Simulation
4.2 Impact on Arrival Times
4.3 Impact on the Bid-ask Spread
4.4 A Remark on Price Returns in the Model
5 Conclusions
References
Price-Time Priority and Pro Rata Matching in an Order Book Model of Financial Markets
1 Introduction
2 Continuous Double Auction and the Definition of the Order Book Model
3 Matching Principles
4 Conclusions
References
High-Frequency Simulations of an Order Book: a Two-scale Approach
1 Introduction
Motivations of Such a Two-layered Model
A Real-life Equivalent of This Model
2 The Macroscopic Scale: a Mean Field Game Model of Agents' Views
2.1 Presentation of the Theoretical Framework
2.2 Modelling Limit Order Books and Price Dynamics
2.3 Calibration and Confrontation to Reality
3 The Microscopic Scale: a Conditioned Zero-intelligence Model
3.1 Main Principles
Conditioning Variables
Marginal Laws
From point process to diffusions
3.2 Choice of Distributions for the Characteristics of Orders
Dataset for Explorations, Illustrations and Fitting
Arrival Rate of Orders
Type of Order
Size of the Next Order
Price of the Next Order (When Needed)
3.3 Overall Simulations
4 Conclusions
References
A Mathematical Approach to Order Book Modelling
1 Introduction and Background
2 An Elementary Approximation: Perfect Market Making
3 Order Book Dynamics
3.1 Model Setup
3.2 Evolution of the Order Book
4 Infinitesimal Generator
5 Price Dynamics
6 Stationary State and Diffusive Limit
6.1 Ergodicity of the Order Book
6.2 Large Scale Limit of the Price
7 Conclusions
References
Appendix A. Lyapunov Stochastic Stability Criterion
Appendix B. Figures
Reconstructing Agents' Strategies from Price Behavior
1 Introduction
2 The Minimal Model
3 The Reconstruction Method
4 Reconstruction for the Agent Model
4.1 Window Size Dependence
4.2 Dependence on the Length of the Moving Average
4.3 Backward Analysis on the Agent Model
5 Analysis on Experimental Data
6 Conclusions and Perspectives
References
Market Influence and Order Book Strategies
1 Properties of the Single Asset Market Model
2 Definition of the Agent-Based Limit Order Book Structure
2.1 Strategic Forces in the Trading Arena
2.2 Price Response to Aggregate Demand
2.3 Learning Strategies for the Fitness Thresholds
2.4 Features of the Model
3 Dynamics and Structure of the Order Book
3.1 Occupation Number Dynamics
3.2 Profile of the Book
3.3 Master Equation
3.4 Robustness of the Results
4 Economic Implications
4.1 Robustness Claim
4.2 Market Impact and Excessive Volatility
4.3 Market Impact and Market Efficiency
4.4 What Are the Effects of Algorithmic Trading?
5 Conclusions
References
Multi-Agent Order Book Simulation: Mono- and Multi-Asset High-Frequency Market Making Strategies
1 Introduction
2 Market Models
2.1 Zero-intelligence Market
2.2 Market with Autocorrelated Order Flow
2.3 Market with Informed Traders
3 High Frequency Market Making Strategies
3.1 Default Strategy
Position Closing
Inventory Limits
Orders Cancellation
3.2 Full Priority
3.3 Spread-based Priority
3.4 Orders Placement Strategy
3.5 Advanced Strategies
3.5.1 Trend Follower
3.5.2 Mean Reversion
4 Analysis
4.1 Zero-intelligence Market
4.2 Autocorrelated Market
4.3 Market with Informed Traders
5 Conclusions and Current Research
References
Part II High-Frequency Data and Modelling
The Nature of Price Returns During Periods of High Market Activity
1 Introduction
2 Data Description
"Perceived" Tick Size and Tick Value
3 Realized Variance versus Number of Trades
4 Single Trade Impact on the Midpoint Price
4.1 Impact on the Return Variance
4.2 Impact on the Return
5 From Fine to Coarse
5.1 Large Scale Conditional Variance and Impact
5.2 Liquidity Decreases when Trading Rate Increases
6 Conclusions
References
Tick Size and Price Diffusion
1 Introduction
2 Literature Review
2.1 Tick Size and Market Microstructure
2.2 Tick Size and Price Properties on Longer Time Scales
3 Tick Size and Price Diffusion
3.1 Return Distribution
3.2 Volatility Clustering
3.3 A Simple Model
3.4 Tick Size and the Subordination Hypothesis
4 Conclusions
References
High Frequency Correlation Modelling
1 Introduction
2 A Model for High Frequency Correlation
2.1 Empirical Fact: the Epps Effect
2.2 Correlated Point Processes as a Model for Correlation
3 Large Scale Limit
4 Conclusions and Further Research
Appendix A
Appendix B
References
The Model with Uncertainty Zones for Ultra High Frequency Prices and Durations: Applications to Statistical Estimation and Mathematical Finance
1 Introduction
1.1 Microstructure Noise
1.2 Additive Microstructure Noise
1.3 Model with Rounding Errors
1.4 Towards a Joint Dynamic for Prices and Durations
2 Model with Uncertainty Zones
2.1 Description of the Model
2.2 Discussion
2.3 Properties of the Last Traded Price and Its Durations
3 Statistical Procedures
3.1 Estimation of the Efficient Price
3.2 Estimation of n
3.3 Estimation of the Integrated Volatility
3.4 Estimation of the Integrated Covariation
4 Hedging Error and Microstructure Noise
4.1 Hedging Strategies
4.1.1 Benchmark Frictionless Hedging Strategy
4.1.2 Hedging Strategies in an Uncertainty Zone Market
4.2 Asymptotic Results for the Hedging Error
4.3 Hedging Error Without Microstructure Noise on the Price
4.4 Hedging Error with Microstructure Noise
4.5 Optimal Rebalancing Level in the Presence of Microstructure Noise
4.6 One Numerical Study
References
Exponential Resilience and Decay of Market Impact
1 Two Different Generalizations of the Obizhaeva and Wang Model
1.1 The Gatheral (JG) Model
1.2 A Version of the Alfonsi-Fruth-Schied (AFS) Model in Continuous Time
2 Price Manipulation in the Gatheral and Alfonsi-Fruth-Schied Models
3 VWAP-equivalent Models
3.1 When Are VWAP-equivalent Models Identical?
4 Compatibility with the Square-root Formula
5 Conclusions
References
Part III Miscellaneous
Modeling the Non-Markovian, Non-stationary Scaling Dynamics of Financial Markets
1 Introduction
2 An Ensemble of Histories Based on the Returns of the EUR/USD Exchange Rate
3 Self-similar Model Process
4 Correlations Structure
5 Conclusions
References
The von Neumann-Morgenstern Utility Functions with Constant Risk Aversions
1 Introduction
2 Preliminaries and Definitions
3 The Characterization Theorems
4 Conclusions
References
Income and Expenditure Distribution. A Comparative Analysis
1 Introduction
2 Theoretical Framework
3 Comparison of Income and Expenditure Distribution
3.1 The Case of Same Parametric Value for Agents
3.2 Asymptotic Case with No Savings and One Dominant Good
3.3 A Simulation Study
4 Discussion
References
Two Agent Allocation Problems and the First Best
1 Introduction
2 The Framework
3 TheResult
4 Conclusions
References
Opinion Formation in a Heterogenous Society
1 Introduction
2 Kinetic Approaches for Opinion Formation
2.1 A Kinetic Model with Several Groups
3 The Limiting Fokker-Planck System
4 Numerical Simulations
4.1 Monte Carlo Simulations
4.2 Numerical Solution of the Fokker-Planck System
4.3 Numerical Examples
5 Conclusions
References
Opinion Formation in the Kinetic Exchange Models
1 Introduction
2 Model for Opinion Formation and Results
2.1 Homogeneous Multi-agent Model
2.2 Random Multiplier Map
2.3 Results and Analyses
3 Discussion and Extension
3.1 Two Parameter Model: Sen
3.2 Lattice Version and Non-equilibrium Relaxation Studies: Biswas et al.
3.3 Heterogeneous Multi-agent Model
References
Panel Discussion
References
New Economic Windows Series

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Econophysics of Order-driven Markets

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