Quantitative trading - algorithms, analytics, data, models, optimization

The first part of this book discusses institutions and mechanisms of algorithmic trading, market microstructure, high-frequency data and stylized facts, time and event aggregation, order book dynamics, trading strategies and algorithms, transaction costs, market impact and execution strategies, risk analysis, and management. The second part covers market impact models, network models, multi-asset trading, machine learning techniques, and nonlinear filtering. The third part discusses electronic market making, liquidity, systemic risk, recent developments and debates on the subject. -- Provided by publisher Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Dedication 6 Contents 8 Preface 14 List of Figures 18 List of Tables 22 1 Introduction 24 1.1 Evolution of trading infrastructure 24 1.2 Quantitative strategies and time-scales 28 1.3 Statistical arbitrage and debates about EMH 29 1.4 Quantitative funds, mutual funds, hedge funds 31 1.5 Data, analytics, models, optimization, algorithms 33 1.6 Interdisciplinary nature of the subject and how the book can be used 34 1.7 Supplements and problems 36 2 Statistical Models and Methods for Quantitative Trading 40 2.1 Stylized facts on stock price data 41 2.1.1 Time series of low-frequency returns 41 2.1.2 Discrete price changes in high-frequency data 41 2.2 Brownian motion models for speculative prices 45 2.3 MPT as a "walking shoe" down Wall Street 45 2.4 Statistical underpinnings of MPT 47 2.4.1 Multifactor pricing models 47 2.4.2 Bayes, shrinkage, and Black-Litterman estimators 48 2.4.3 Bootstrapping and the resampled frontier 49 2.5 A new approach incorporating parameter uncertainty 50 2.5.1 Solution of the optimization problem 50 2.5.2 Computation of the optimal weight vector 51 2.5.3 Bootstrap estimate of performance and NPEB 52 2.6 From random walks to martingales that match stylized facts 53 2.6.1 From Gaussian to Paretian random walks 54 2.6.2 Random walks with optional sampling times 55 2.6.3 From random walks to ARIMA, GARCH 58 2.7 Neo-MPT involving martingale regression models 60 2.7.1 Incorporating time series effects in NPEB 61 2.7.2 Optimizing information ratios along efficient frontier 61 2.7.3 An empirical study of neo-MPT 62 2.8 Statistical arbitrage and strategies beyond EMH 64 2.8.1 Technical rules and the statistical background 64 2.8.2 Time series, momentum, and pairs trading strategies 66 2.8.3 Contrarian strategies, behavioral finance, and investors' cognitive biases 67 2.8.4 From value investing to global macro strategies 67 2.8.5 In-sample and out-of-sample evaluation 68 2.9 Supplements and problems 69 3 Active Portfolio Management and Investment Strategies 84 3.1 Active alpha and beta in portfolio management 85 3.1.1 Sources of alpha 86 3.1.2 Exotic beta beyond active alpha 86 3.1.3 A new approach to active portfolio optimization 87 3.2 Transaction costs, and long-short constraints 90 3.2.1 Cost of transactions and its components 90 3.2.2 Long-short and other portfolio constraints 91 3.3 Multiperiod portfolio management 92 3.3.1 The Samuelson-Merton theory 92 3.3.2 Incorporating transaction costs into Merton's problem 95 3.3.3 Multiperiod capital growth and volatility pumping 96 3.3.4 Multiperiod mean-variance portfolio rebalancing 97 3.3.5 Dynamic mean-variance portfolio optimization 98 3.3.6 Dynamic portfolio selection 99 3.4 Supplementary notes and comments 101 3.5 Exercises 124 4 Econometrics of Transactions in Electronic Platforms 126 4.1 Transactions and transactions data 127 4.2 Models for high-frequency data 127 4.2.1 Roll's model of bid-ask bounce 128 4.2.2 Market microstructure model with additive noise 129 4.3 Estimation of integrated variance of X[sub(t)] 130 4.3.1 Sparse sampling methods 131 4.3.2 Averaging method over subsamples 132 4.3.3 Method of two time-scales 132 4.3.4 Method of kernel smoothing: Realized kernels 133 4.3.5 Method of pre-averaging 134 4.3.6 From MLE of volatility parameter to QMLE of [X][sub(T)] 135 4.4 Estimation of covariation of multiple assets 136 4.4.1 Asynchronicity and the Epps effect 136 4.4.2 Synchronization procedures 137 4.4.3 QMLE for covariance and correlation estimation 138 4.4.4 Multivariate realized kernels and two-scale estimators 139 4.5 Fourier methods 141 4.5.1 Fourier estimator of [X][sub(T)] and spot volatility 141 4.5.2 Statistical properties of Fourier estimators 143 4.5.3 Fourier estimators of spot co-volatilities 144 4.6 Other econometric models involving TAQ 145 4.6.1 ACD models of inter-transaction durations 146 4.6.2 Self-exciting point process models 147 4.6.3 Decomposition of D[sub(i)] and generalized linear models 148 4.6.4 McCulloch and Tsay's decomposition 149 4.6.5 Joint modeling of point process and its marks 150 4.6.6 Realized GARCH and other predictive models 151 4.6.7 Jumps in efficient price process and power variation 153 4.7 Supplementary notes and comments 155 4.8 Exercises 162 5 Limit Order Book: Data Analytics and Dynamic Models 166 5.1 From market data to limit order book (LOB) 167 5.2 Stylized facts of LOB data 168 5.2.1 Book price adjustment 168 5.2.2 Volume imbalance and other indicators 171 5.3 Fitting a multivariate point process to LOB data 174 5.3.1 Marketable orders as a multivariate point process 174 5.3.2 Empirical illustration 176 5.4 LOB data analytics via machine learning 180 5.5 Queueing models of LOB dynamics 182 5.5.1 Diffusion limits of the level-1 reduced-form model 183 5.5.2 Fluid limit of order positions 186 5.5.3 LOB-based queue-reactive model 189 5.6 Supplements and problems 192 6 Optimal Execution and Placement 206 6.1 Optimal execution with a single asset 207 6.1.1 Dynamic programming solution of problem (6.2) 208 6.1.2 Continuous-time models and calculus of variations 210 6.1.3 Myth: Optimality of deterministic strategies 212 6.2 Multiplicative price impact model 213 6.2.1 The model and stochastic control problem 213 6.2.2 HJB equation for the finite-horizon case 214 6.2.3 Infinite-horizon case T = 8 216 6.2.4 Price manipulation and transient price impact 219 6.3 Optimal execution using the LOB shape 219 6.3.1 Cost minimization 222 6.3.2 Optimal strategy for Model 1 225 6.3.3 Optimal strategy for Model 2 226 6.3.4 Closed-form solution for block-shaped LOBs 227 6.4 Optimal execution for portfolios 227 6.5 Optimal placement 230 6.5.1 Markov random walk model with mean reversion 231 6.5.2 Continuous-time Markov chain model 234 6.6 Supplements and problems 238 7 Market Making and Smart Order Routing 244 7.1 Ho and Stoll's model and the Avellanedo-Stoikov policy 245 7.2 Solution to the HJB equation and subsequent extensions 246 7.3 Impulse control involving limit and market orders 248 7.3.1 Impulse control for the market maker 248 7.3.2 Control formulation 249 7.4 Smart order routing and dark pools 251 7.5 Optimal order splitting among exchanges in SOR 253 7.5.1 The cost function and optimization problem 254 7.5.2 Optimal order placement across K exchanges 255 7.5.3 A stochastic approximation method 256 7.6 Censored exploration-exploitation for dark pools 257 7.6.1 The SOR problem and a greedy algorithm 257 7.6.2 Modified Kaplan-Meier estimate T[sub(i)] 258 7.6.3 Exploration, exploitation, and optimal allocation 259 7.7 Stochastic Lagrangian optimization in dark pools 260 7.7.1 Lagrangian approach via stochastic approximation 261 7.7.2 Convergence of Lagrangian recursion to optimizer 263 7.8 Supplementary notes and comments 264 7.9 Exercises 271 8 Informatics, Regulation and Risk Management 274 8.1 Some quantitative strategies 276 8.2 Exchange infrastructure 278 8.2.1 Order gateway 281 8.2.2 Matching engine 281 8.2.3 Market data dissemination 282 8.2.4 Order fee structure 283 8.2.5 Colocation service 285 8.2.6 Clearing and settlement 286 8.3 Strategy informatics and infrastructure 287 8.3.1 Market data handling 287 8.3.2 Alpha engine 288 8.3.3 Order management 289 8.3.4 Order type and order qualifier 289 8.4 Exchange rules and regulations 292 8.4.1 SIP and Reg NMS 292 8.4.2 Regulation SHO 295 8.4.3 Other exchange-specific rules 296 8.4.4 Circuit breaker 297 8.4.5 Market manipulation 297 8.5 Risk management 297 8.5.1 Operational risk 298 8.5.2 Strategy risk 300 8.6 Supplementary notes and comments 302 8.7 Exercises 312 A: Martingale Theory 318 A.1 Discrete-time martingales 318 A.2 Continuous-time martingales 321 B: Markov Chain and Related Topics 326 B.1 Generator Q of CTMC 326 B.2 Potential theory for Markov chains 327 B.3 Markov decision theory 327 C: Doubly Stochastic Self-Exciting Point Processes 330 C.1 Martingale theory and compensators of multivariate counting processes 330 C.2 Doubly stochastic point process models 331 C.3 Likelihood inference in point process models 332 C.4 Simulation of doubly stochastic SEPP 335 D: Weak Convergence and Limit Theorems 338 D.1 Donsker's theorem and its extensions 339 D.2 Queuing system and limit theorems 340 Bibliography 342 Index 372 Introduction Evolution of trading infrastructure Quantitative strategies and time-scalesStatistical arbitrage and debates about EMH Quantitative funds, mutual funds, hedge fundsData, analytics, models, optimization, algorithms Interdisciplinary nature of the subject and how the book can be used Supplements and problems Statistical Models and Methods for Quantitative Trading Stylized facts on stock price data Time series of low-frequency returnsDiscrete price changes in high-frequency dataBrownian motion at the Paris Exchange and random walk down Wall Street MPT as a \walking shoe" down Wall Street Statistical underpinnings of MPT Multifactor pricing models Bayes, shrinkage, and Black-Litterman estimatorsBootstrapping and the resampled frontierA new approach incorporating parameter uncertainty Solution of the optimization problem Computation of the optimal weight vector Bootstrap estimate of performance and NPEBFrom random walks to martingales that match stylized facts From Gaussian to Paretian random walksRandom walks with optional sampling timesFrom random walks to ARIMA, GARCH Neo-MPT involving martingale regression modelsIncorporating time series e_ects in NPEB Optimizing information ratios along e_cient frontier An empirical study of neo-MPT Statistical arbitrage and strategies beyond EMH Technical rules and the statistical backgroundTime series, momentum, and pairs trading strategies Contrarian strategies, behavioral _nance, and investors' cognitive biases From value investing to global macro strategies In-sample and out-of-sample evaluationSupplements and problems 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 Components of cost of transactionLong-short and other portfolio constraints Multiperiod portfolio management The Samuelson-Merton theoryIncorporating 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 ExercisesEconometrics of Transactions in Electronic Platforms Transactions and transactions dataModels for high-frequency dataRoll's model of bid-ask bounce Market microstructure model with additive noiseEstimation of integrated variance of XtSparse sampling methodsAveraging method over subsamples Method of two time-scales Method of kernel smoothing: Realized kernels Method of pre-averagingFrom MLE of volatility parameter to QMLE of [X]T Estimation of covariation of multiple assetsAsynchronicity and the Epps effect Synchronization proceduresQMLE for covariance and correlation estimation Multivariate realized kernels and two-scale estimators Fourier methods Fourier estimator of [X]T and spot volatilityStatistical properties of Fourier estimatorsFourier estimators of spot co-volatilities Other econometric models involving TAQACD models of inter-transaction durations Self-exciting point process modelsDecomposition of Di and generalized linear models Joint modeling of point process and its marksMcCulloch and Tsay's decompositionRealized GARCH and other predictive modelsJumps in e_cient price process and power variationSupplementary 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 adjustmentVolume imbalance and other indicators Fitting a multivariate point process to LOB data Marketable orders as a multivariate point process Empirical illustrationLOB data analytics via machine learningQueueing 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 assetDynamic programming solution of problem (6.2) Continuous-time models and calculus of variations Myth{the optimal deterministic strategies Multiplicative price impact model The model and stochastic control problem HJB equation for _nite-horizon case In_nite-horizon case T = 1 Price manipulation and transient price impactOptimal execution with LOBCost minimization Optimal strategy for Model 1Optimal strategy for Model 2 Closed-form solution for block-shaped LOBsOptimal execution with portfoliosOptimal placement Markov random walk model with mean reversion Continuous-time Markov chain model Supplements and problemsMarket Making and Smart Order Routing Ho and Stoll's model and the Avellanedo-Stoikov policy Solution to the HJB equation and subsequent extensions Impulse control involving limit and market ordersImpulse control for the market Control formulation Smart order routing and dark poolsOptimal order splitting among exchanges in SOR The cost function and optimization problem Optimal order placement across K exchangesA stochastic approximation methodCensored exploration-exploitation for dark pools The SOR problem and a greedy algorithm Modi_ed Kaplan-Meier estimate ^ Ti 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 ExercisesInformatics, Regulation and Risk Management Some quantitative strategiesExchange infrastructureOrder gatewayMatching engine Market data disseminationOrder fee structure Colocation service Clearing and settlement Strategy informatics and infrastructure Market data handling Alpha engine Order managementOrder type and order qualifierExchange rules and regulationsSIP and Reg NMSRegulation SHO Other exchange-specific rules Circuit breakerMarket manipulationRisk management Operational risk Strategy risk Supplementary notes and comments ExercisesA Martingale Theory Discrete-time martingales Continuous-time martingalesMarkov Chain and Related Topics Generator Q of CTMCPotential theory for Markov chainsMarkov decision theory Doubly Stochastic Self-Exciting Point Processes Martingale theory, intensity process, self-excitation Hawkes process: Compensator and stationarityEstimation in point process models Asymptotic theory and likelihood inference Simulation of doubly stochastic SEPPWeak Convergence and Limit Theorems Donsker's theorem and its extensions Queuing system and limit theorems