لایب سان

Author(s): Wong, Samuel Po Shing

Publisher: Taylor & Francis Inc, Year: 2016

ISBN: 9781498706483,1498706487

Contents Preface xiii List of Figures xvii List of Tables xxi 1 Introduction 1 1.1 Evolution of trading infrastructure . . . . . . . . . . . . . . . 1 1.2 Quantitative strategies and time-scales . . . . . . . . . . . . 5 1.3 Statistical arbitrage and debates about EMH . . . . . . . . . 6 1.4 Quantitative funds, mutual funds, hedge funds . . . . . . . . 8 1.5 Data, analytics, models, optimization, algorithms . . . . . . 10 1.6 Interdisciplinary nature of the subject and how the book can be used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.7 Supplements and problems . . . . . . . . . . . . . . . . . . . 13 2 Statistical Models and Methods for Quantitative Trading 17 2.1 Stylized facts on stock price data . . . . . . . . . . . . . . . . 18 2.1.1 Time series of low-frequency returns . . . . . . . . . . 18 2.1.2 Discrete price changes in high-frequency data . . . . . 18 2.2 Brownian motion models for speculative prices . . . . . . . . 22 2.3 MPT as a “walking shoe” down Wall Street . . . . . . . . . 22 2.4 Statistical underpinnings of MPT . . . . . . . . . . . . . . . 24 2.4.1 Multifactor pricing models . . . . . . . . . . . . . . . . 24 2.4.2 Bayes, shrinkage, and Black-Litterman estimators . . 25 2.4.3 Bootstrapping and the resampled frontier . . . . . . . 26 2.5 A new approach incorporating parameter uncertainty . . . . 27 2.5.1 Solution of the optimization problem . . . . . . . . . . 27 2.5.2 Computation of the optimal weight vector . . . . . . . 28 2.5.3 Bootstrap estimate of performance and NPEB . . . . 29 2.6 From random walks to martingales that match stylized facts 30 2.6.1 From Gaussian to Paretian random walks . . . . . . . 31 2.6.2 Random walks with optional sampling times . . . . . 32 2.6.3 From random walks to ARIMA, GARCH . . . . . . . 35 2.7 Neo-MPT involving martingale regression models . . . . . . 37 vii viii Contents 2.7.1 Incorporating time series effects in NPEB . . . . . . . 38 2.7.2 Optimizing information ratios along efficient frontier . 38 2.7.3 An empirical study of neo-MPT . . . . . . . . . . . . 39 2.8 Statistical arbitrage and strategies beyond EMH . . . . . . . 41 2.8.1 Technical rules and the statistical background . . . . . 41 2.8.2 Time series, momentum, and pairs trading strategies . 43 2.8.3 Contrarian strategies, behavioral finance, and investors’ cognitive biases . . . . . . . . . . . . . . . . . . . . . . 44 2.8.4 From value investing to global macro strategies . . . . 44 2.8.5 In-sample and out-of-sample evaluation . . . . . . . . 45 2.9 Supplements and problems . . . . . . . . . . . . . . . . . . . 46 3 Active Portfolio Management and Investment Strategies 61 3.1 Active alpha and beta in portfolio management . . . . . . . 62 3.1.1 Sources of alpha . . . . . . . . . . . . . . . . . . . . . 63 3.1.2 Exotic beta beyond active alpha . . . . . . . . . . . . 63 3.1.3 A new approach to active portfolio optimization . . . 64 3.2 Transaction costs, and long-short constraints . . . . . . . . . 67 3.2.1 Cost of transactions and its components . . . . . . . . 67 3.2.2 Long-short and other portfolio constraints . . . . . . . 68 3.3 Multiperiod portfolio management . . . . . . . . . . . . . . . 69 3.3.1 The Samuelson-Merton theory . . . . . . . . . . . . . 69 3.3.2 Incorporating transaction costs into Merton’s problem 72 3.3.3 Multiperiod capital growth and volatility pumping . . 73 3.3.4 Multiperiod mean-variance portfolio rebalancing . . . 74 3.3.5 Dynamic mean-variance portfolio optimization . . . . 75 3.3.6 Dynamic portfolio selection . . . . . . . . . . . . . . . 76 3.4 Supplementary notes and comments . . . . . . . . . . . . . . 78 3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4 Econometrics of Transactions in Electronic Platforms 103 4.1 Transactions and transactions data . . . . . . . . . . . . . . 104 4.2 Models for high-frequency data . . . . . . . . . . . . . . . . . 104 4.2.1 Roll’s model of bid-ask bounce . . . . . . . . . . . . . 105 4.2.2 Market microstructure model with additive noise . . . 106 4.3 Estimation of integrated variance of Xt . . . . . . . . . . . . 107 4.3.1 Sparse sampling methods . . . . . . . . . . . . . . . . 108 4.3.2 Averaging method over subsamples . . . . . . . . . . . 109 4.3.3 Method of two time-scales . . . . . . . . . . . . . . . . 109 4.3.4 Method of kernel smoothing: Realized kernels . . . . . 110 4.3.5 Method of pre-averaging . . . . . . . . . . . . . . . . . 111 4.3.6 From MLE of volatility parameter to QMLE of [X]T . 112 4.4 Estimation of covariation of multiple assets . . . . . . . . . . 113 Contents ix 4.4.1 Asynchronicity and the Epps effect . . . . . . . . . . . 113 4.4.2 Synchronization procedures . . . . . . . . . . . . . . . 114 4.4.3 QMLE for covariance and correlation estimation . . . 115 4.4.4 Multivariate realized kernels and two-scale estimators 116 4.5 Fourier methods . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.5.1 Fourier estimator of [X]T and spot volatility . . . . . 118 4.5.2 Statistical properties of Fourier estimators . . . . . . . 120 4.5.3 Fourier estimators of spot co-volatilities . . . . . . . . 121 4.6 Other econometric models involving TAQ . . . . . . . . . . . 122 4.6.1 ACD models of inter-transaction durations . . . . . . 123 4.6.2 Self-exciting point process models . . . . . . . . . . . 124 4.6.3 Decomposition of Di and generalized linear models . . 125 4.6.4 McCulloch and Tsay’s decomposition . . . . . . . . . 126 4.6.5 Joint modeling of point process and its marks . . . . . 127 4.6.6 Realized GARCH and other predictive models . . . . 128 4.6.7 Jumps in efficient price process and power variation . 130 4.7 Supplementary notes and comments . . . . . . . . . . . . . . 132 4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5 Limit Order Book: Data Analytics and Dynamic Models 143 5.1 From market data to limit order book (LOB) . . . . . . . . . 144 5.2 Stylized facts of LOB data . . . . . . . . . . . . . . . . . . . 145 5.2.1 Book price adjustment . . . . . . . . . . . . . . . . . . 145 5.2.2 Volume imbalance and other indicators . . . . . . . . 148 5.3 Fitting a multivariate point process to LOB data . . . . . . . 151 5.3.1 Marketable orders as a multivariate point process . . . 151 5.3.2 Empirical illustration . . . . . . . . . . . . . . . . . . 153 5.4 LOB data analytics via machine learning . . . . . . . . . . . 157 5.5 Queueing models of LOB dynamics . . . . . . . . . . . . . . 159 5.5.1 Diffusion limits of the level-1 reduced-form model . . . 160 5.5.2 Fluid limit of order positions . . . . . . . . . . . . . . 163 5.5.3 LOB-based queue-reactive model . . . . . . . . . . . . 166 5.6 Supplements and problems . . . . . . . . . . . . . . . . . . . 169 6 Optimal Execution and Placement 183 6.1 Optimal execution with a single asset . . . . . . . . . . . . . 184 6.1.1 Dynamic programming solution of problem (6.2) . . . 185 6.1.2 Continuous-time models and calculus of variations . . 187 6.1.3 Myth: Optimality of deterministic strategies . . . . . . 189 6.2 Multiplicative price impact model . . . . . . . . . . . . . . . 190 6.2.1 The model and stochastic control problem . . . . . . . 190 6.2.2 HJB equation for the finite-horizon case . . . . . . . . 191 6.2.3 Infinite-horizon case T = ∞ . . . . . . . . . . . . . . . 193 x Contents 6.2.4 Price manipulation and transient price impact . . . . 196 6.3 Optimal execution using the LOB shape . . . . . . . . . . . 196 6.3.1 Cost minimization . . . . . . . . . . . . . . . . . . . . 199 6.3.2 Optimal strategy for Model 1 . . . . . . . . . . . . . . 202 6.3.3 Optimal strategy for Model 2 . . . . . . . . . . . . . . 203 6.3.4 Closed-form solution for block-shaped LOBs . . . . . . 204 6.4 Optimal execution for portfolios . . . . . . . . . . . . . . . . 204 6.5 Optimal placement . . . . . . . . . . . . . . . . . . . . . . . 207 6.5.1 Markov random walk model with mean reversion . . . 208 6.5.2 Continuous-time Markov chain model . . . . . . . . . 211 6.6 Supplements and problems . . . . . . . . . . . . . . . . . . . 215 7 Market Making and Smart Order Routing 221 7.1 Ho and Stoll’s model and the Avellanedo-Stoikov policy . . . 222 7.2 Solution to the HJB equation and subsequent extensions . . 223 7.3 Impulse control involving limit and market orders . . . . . . 225 7.3.1 Impulse control for the market maker . . . . . . . . . 225 7.3.2 Control formulation . . . . . . . . . . . . . . . . . . . 226 7.4 Smart order routing and dark pools . . . . . . . . . . . . . . 228 7.5 Optimal order splitting among exchanges in SOR . . . . . . 230 7.5.1 The cost function and optimization problem . . . . . . 231 7.5.2 Optimal order placement across K exchanges . . . . . 232 7.5.3 A stochastic approximation method . . . . . . . . . . 233 7.6 Censored exploration-exploitation for dark pools . . . . . . . 234 7.6.1 The SOR problem and a greedy algorithm . . . . . . . 234 7.6.2 Modified Kaplan-Meier estimate ˆTi . . . . . . . . . . . 235 7.6.3 Exploration, exploitation, and optimal allocation . . . 236 7.7 Stochastic Lagrangian optimization in dark pools . . . . . . 237 7.7.1 Lagrangian approach via stochastic approximation . . 238 7.7.2 Convergence of Lagrangian recursion to optimizer . . 240 7.8 Supplementary notes and comments . . . . . . . . . . . . . . 241 7.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 8 Informatics, Regulation and Risk Management 251 8.1 Some quantitative strategies . . . . . . . . . . . . . . . . . . 253 8.2 Exchange infrastructure . . . . . . . . . . . . . . . . . . . . . 255 8.2.1 Order gateway . . . . . . . . . . . . . . . . . . . . . . 258 8.2.2 Matching engine . . . . . . . . . . . . . . . . . . . . . 258 8.2.3 Market data dissemination . . . . . . . . . . . . . . . 259 8.2.4 Order fee structure . . . . . . . . . . . . . . . . . . . . 260 8.2.5 Colocation service . . . . . . . . . . . . . . . . . . . . 262 8.2.6 Clearing and settlement . . . . . . . . . . . . . . . . . 263 8.3 Strategy informatics and infrastructure . . . . . . . . . . . . 264 Contents xi 8.3.1 Market data handling . . . . . . . . . . . . . . . . . . 264 8.3.2 Alpha engine . . . . . . . . . . . . . . . . . . . . . . . 265 8.3.3 Order management . . . . . . . . . . . . . . . . . . . . 266 8.3.4 Order type and order qualifier . . . . . . . . . . . . . 266 8.4 Exchange rules and regulations . . . . . . . . . . . . . . . . . 269 8.4.1 SIP and Reg NMS . . . . . . . . . . . . . . . . . . . . 269 8.4.2 Regulation SHO . . . . . . . . . . . . . . . . . . . . . 272 8.4.3 Other exchange-specific rules . . . . . . . . . . . . . . 273 8.4.4 Circuit breaker . . . . . . . . . . . . . . . . . . . . . . 274 8.4.5 Market manipulation . . . . . . . . . . . . . . . . . . . 274 8.5 Risk management . . . . . . . . . . . . . . . . . . . . . . . . 274 8.5.1 Operational risk . . . . . . . . . . . . . . . . . . . . . 275 8.5.2 Strategy risk . . . . . . . . . . . . . . . . . . . . . . . 277 8.6 Supplementary notes and comments . . . . . . . . . . . . . . 279 8.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 A Martingale Theory 295 A.1 Discrete-time martingales . . . . . . . . . . . . . . . . . . . . 295 A.2 Continuous-time martingales . . . . . . . . . . . . . . . . . . 298 B Markov Chain and Related Topics 303 B.1 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.1 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.1 Donsker’s theorem and its extensions . . . . . . . . . . . . . 316 D.2 Queuing system and limit theorems . . . . . . . . . . . . . . 317 Bibliography 319 Index 349

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