Algorithms, Analytics, Data, Models, Optimization. Xin Guo University of California, Berkeley, USA. Tze Leung Lai Stanford University, California, USA

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1 QUANTITATIVE TRADING Algorithms, Analytics, Data, Models, Optimization Xin Guo University of California, Berkeley, USA Tze Leung Lai Stanford University, California, USA Howard Shek Tower Research Capital, New York City, New York, USA Samuel Po-Shing Wong 5Lattice Securities Limited, Hong Kong, China CRC Press Taylor & Francis Group Bora Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an Informa business A CHAPMAN Sc HALL BOOK

2 Contents Preface List of Figures List of Tables xiii xvii xxi 1 Introduction Evolution of trading infrastructure Quantitative strategies and time-scales Statistical arbitrage and debates about EMH Quantitative funds, mutual funds, hedge funds Data, analytics, models, optimization, algorithms Interdisciplinary nature of the subject and how the book can be used Supplements and problems 13 2 Statistical Models and Methods for Quantitative Trading Stylized facta on stock price data Time series of low-frequency returns Discrete price changes in high-frequency data Brownian motion models for speculative prices MPT as a "walking shoe" down Wall Street Statistical underpinnings of MPT Multifactor pricing models Bayes, shrinkage, and Black-Litterman estimators Bootstrapping and the resampled frontier A new approach incorporating parameter uncertainty Solution of the optimization problem Computation of the optimal weight vector Bootstrap estimate of Performance and NPEB From random walks to martingales that match stylized facts From Gaussian to Paretian random walks Random walks with optional sampling times From random walks to ARIMA, GARCH Neo-MPT involving martingale regression models 37 vii

3 viii Contents Incorporating time series effects in NPEB Optimizing Information ratios along efficient frontier An empirical study of neo-mpt Statistical arbitrage and strategies beyond EMH Technical rules and the Statistical background Time series, momentum, and pairs trading strategies Contrarian strategies, behavioral ßnance, and Investors' cognitive biases From value investing to global macro strategies In-sample and out-of-sample evaluation Supplements and problems 46 3 Active Portfolio Management and Investment Strategies Active alpha and beta in portfolio management Sources of alpha Exotic beta beyond active alpha A new approach to active portfolio optimization Transaction costs, and long-short constraints Cost of transactions and its components Long-short and other portfolio constraints Multiperiod portfolio management The Samuelson-Merton theory Incorporating transaction costs into Merton's problem Multiperiod capital growth and volatility pumping Multiperiod mean-variance portfolio rebalancing Dynamic mean-variance portfolio optimization Dynamic portfolio selection Supplementary notes and comments Exercises Econometrics of Transactions in Electronic Platforms Transactions and transactions data Models for high-frequency data Roll's model of bid-ask bounce Market microstructure model with additive noise Estimation of integrated variance of X t Sparse sampling methods Averaging method over subsamples Method of two time-scales Method of kernel smoothing: Realized kernels Method of pre-averaging From MLE of volatility parameter to QMLE of [X) T Estimation of covariation of multiple assets 113

4 Contents ix Asynchronicity and the Epps effect Synchronization procedures QMLE for covariance and correlation estimation Multivariate realized kernels and two-scale estimators Fourier methods Fourier estimator of [X\T and spot volatility Statistical properties of Fourier estimators Fourier estimators of spot co-volatilities Other econometric models involving TAQ ACD models of inter-transaction durations Self-exciting point process models Decomposition of Di and generalized linear models McCulloch and Tsay's decomposition Joint modeling of point process and its marks Realized GARGE and other predictive models Jumps in efficient price process and power Variation Supplementary notes and comments Exercises Limit Order Book: Data Analytics and Dynamic Models From market data to limit Order book (LOB) Stylized facts of LOB data Book price adjustment Volume imbalance and other indicators Fitting a multivariate point process to LOB data Marketable Orders as a multivariate point process Empirical Illustration LOB data analytics via machine learning Queueing models of LOB dynamics Diffusion limits of the level-1 reduced-form model Fluid limit of order positions LOB-based queue-reactive model Supplements and problems Optimal Execution and Placement Optimal execution with a single asset Dynamic programming Solution of problem (6.2) Continuous-time models and calculus of variations Myth: Optimality of deterministic strategies Multiplicative price impact model The model and stochastic control problem HJB equation for the ffnite-horizon case Inffnite-horizon case T oo 193

5 X Contents Price manipulation and transient price impact Optimal execution using the LOB shape Cost minimization Optimal strategy for Model Optimal strategy for Model Closed-form Solution for block-shaped LOBs Optimal execution for portfolios Optimal placement, Markov random walk model with mean reversion Continuous-time Markov chain model Supplements and problems Market Making and Smart Order Routing Ho and Stoibs model and the Avellanedo-Stoikov policy Solution to the HJB equation and subsequent extensions Impulse control involving limit and market Orders Impulse control for the market maker Control formulation Smart order routing and dark pools Optimal order Splitting among exchanges in SOR The cost function and optimization problem Optimal order placement across K exchanges A stochastic approximation method Censored exploration-exploitation for dark pools The SOR problem and a greedy algorithm Modified Kaplan-Meier estimate Tj Exploration, exploitation, and optimal allocation Stochastic Lagrangian optimization in dark pools Lagrangian approach via stochastic approximation Convergence of Lagrangian recursion to optimizer Supplementary notes and comments Exercises Informatics, Regulation and Risk Management Some quantitative strategies Exchange infrastructure Order gateway Malching engine Market data dissemination Order fee structure Colocation Service Clearing and settlement Strategy informatics and infrastructure 264

6 Contents xi Market data handling Alpha engine Order management Order type and order qualifier Exchange rules and regulations SIP and Reg NMS Regulation SHO Other exchange-specific rules Circuit breaker Market manipulation Risk management Operational risk Strategy risk Supplementary notes and comments Exercises 289 A Martingale Theory 295 A.l Discrete-time martingales 295 A.2 Continuous-time martingales 298 B Markov Chain and Related Topics 303 B.l Generator Q of CTMC 303 B.2 Potential theory for Markov chains 304 B.3 Markov decision theory 304 C Doubly Stochastic Self-Exciting Point Processes 307 C.l Martingale theory and compensators of multivariate counting processes 307 C.2 Doubly stochastic point process models 308 C.3 Likelihood inference in point process models 309 C.4 Simulation of doubly stochastic SEPP 312 D Weak Convergence and Limit Theorems 315 D.l Donsker's theorem and its extensions 316 D.2 Queuing system and limit theorems 317 Bibliography 319 Index 349