Introduction About the Editors PART I ECONOMIC MICROSTRUCTURE THEORY 1 Algorithmic Trading: Issues and Preliminary Evidence Thierry Foucault 1.1 Introduction 1.2 What is algorithmic trading? 1.2.1 Definition and typology 1.2.2 Scope and profitability 1.3 Market structure and algorithmic trading 1.4 Costs and benefits of algorithmic trading 1.4.1 Algorithmic trading reduces search costs 1.4.2 Algorithmic trading has an ambiguous effect on adverse selection costs 1.4.3 Algorithmic trading and price discovery 1.4.4 Welfare effects 1.4.5 Algorithmic trading as a source of risk 1.5 Empirical evidence 1.5.1 Algorithmic trading and market liquidity 1.5.2 Algorithmic trading and volatility 1.5.3 Algorithmic trading and price discovery 1.5.4 Algorithmic trading and market stability 1.6 Conclusions Appendix Acknowledgment References 2 Order Choice and Information in Limit Order Markets 41 Ioanid Ro u 2.1 Introduction 2.2 Order choice with symmetric information 2.3 Order choice with asymmetric information 2.4 The information content of orders 2.5 Questions for future research References PART II HIGH FREQUENCY DATA MODELING 3 Some Recent Results on High Frequency Correlation Nicolas Huth and Frederic Abergel 3.1 Introduction 3.2 Data description 3.3 Multivariate event time 3.3.1 Univariate case 3.3.2 Multivariate case 3.3.3 Empirical results 3.4 High frequency lead/lag 3.4.1 The Hayashi--Yoshida cross-correlation function 3.4.2 Empirical results 3.5 Intraday seasonality of correlation 3.5.1 Empirical results 3.6 Conclusion Acknowledgment References 4 Statistical Inference for Volatility and Related Limit Theorems Nakahiro Yoshida 4.1 Introduction 4.2 QLA for an ergodic diffusion process 4.3 QLA for volatility in the finite time-horizon 4.4 Nonsynchronous covariance estimation 4.4.1 Consistent estimator 4.4.2 Functional limit theorem 4.4.3 Application of YUIMA 4.4.4 Lead--lag estimation 4.5 YUIMA II for statistical analysis and simulation for stochastic differential equations 4.6 Higher order asymptotics and finance 4.6.1 Martingale expansion 4.6.2 Small sigma expansion Acknowledgments References PART III MARKET IMPACT 5 Models for the Impact of All Order Book Events Zoltan Eisler, Jean-Philippe Bouchaud, and Julien Kockelkoren 5.1 Introduction 5.2 A short summary of market order impact models 5.3 Many-event impact models 5.3.1 Notation and definitions 5.3.2 The transient impact model (TIM) 5.3.3 The history dependent impact model (HDIM) 5.4 Model calibration and empirical tests 5.4.1 Data 5.4.2 The case of large ticks 5.4.3 The case of small ticks 5.5 Conclusion Appendix Acknowledgments References 6 Limit Order Flow, Market Impact, and Optimal Order Sizes: Evidence from NASDAQ TotalView-ITCH Data Nikolaus Hautsch and Ruihong Huang 6.1 Introduction 6.2 Market environment and data 6.3 Major order flow and order book characteristics 6.4 An econometric model for the market impact of limit orders 6.4.1 A cointegrated VAR model for the limit order book 6.4.2 Estimating market impact 6.5 Market impact at NASDAQ 6.6 Optimal order size 6.7 Conclusions Acknowledgment References PART IV OPTIMAL TRADING Introduction: Trading and Market Micro-structure Charles-Albert Lehalle References 7 Collective Portfolio Optimization in Brokerage Data: The Role of Transaction Cost Structure Damien Challet and David Morton de Lachapelle 7.1 Introduction 7.2 Description of the data 7.3 Results 7.4 The influence of transaction costs on trading behaviour from optimal mean-variance portfolios 7.5 Discussion and outlook Acknowledgments References 8 Optimal Execution of Portfolio Transactions with Short-Term Alpha Adriana M. Criscuolo and Henri Waelbroeck 8.1 Introduction 8.2 Short-term alpha decay and hidden order arbitrage theory 8.3 Total cost definition and constraints 8.3.1 Equations without the risk term 8.3.2 Equations including risk without the alpha term 8