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.

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

Statistical Models and Methods for Quantitative Trading

Stylized facts on stock price data

Time series of low-frequency returns

Discrete price changes in high-frequency data

Brownian 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 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

Incorporating 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 background

Time 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 evaluation

Supplements 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 transaction

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 Xt

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

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

Joint modeling of point process and its marks

McCulloch and Tsay's decomposition

Realized GARCH and other predictive models

Jumps in e_cient 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{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 impact

Optimal execution with LOB

Cost minimization

Optimal strategy for Model 1

Optimal strategy for Model 2

Closed-form solution for block-shaped LOBs

Optimal execution with 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 Stoll's 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

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

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

Exercises

Informatics, Regulation and Risk Management

Some quantitative strategies

Exchange infrastructure

Order gateway

Matching engine

Market data dissemination

Order fee structure

Colocation service

Clearing and settlement

Strategy informatics and infrastructure

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

A Martingale Theory

Discrete-time martingales

Continuous-time martingales

Markov Chain and Related Topics

Generator Q of CTMC

Potential theory for Markov chains

Markov decision theory

Doubly Stochastic Self-Exciting Point Processes

Martingale theory, intensity process, self-excitation

Hawkes process: Compensator and stationarity

Estimation in point process models

Asymptotic theory and likelihood inference

Simulation of doubly stochastic SEPP

Weak Convergence and Limit Theorems

Donsker's theorem and its extensions

Queuing system and limit theorems

Xin Guo is the Coleman Fung Chair Professor of Financial Modeling in the department of Industrial Engineering and Operations Research, UC Berkeley. She founded the Berkeley Risk Analysis and Data Analytics Research (RADAR) Lab and holds a courtesy appointment with the Lawrence Berkeley National Lab. Prior to UC Berkeley, she was a Research Staff Member at the IBM T. J. Watson Research Center and an Associate Professor at Cornell University. Her main research interests are stochastic control, stochastic processes and applications. In addition to high frequency trading modeling and analysis, her recent research includes singular controls, impulse controls, non-linear expectations, mean-field games, and filtration enlargement with application to credit risk.

Tze Leung Lai is a Professor of Statistics and, by courtesy, of Health Research and Policy in the School of Medicine and of the Institute for Computational & Mathematical Engineering (ICME) in the School of Engineering at Stanford University. He is Director of the Financial and Risk Modeling Institute, Co-Director of the Biostatistics Core of the Stanford Cancer Institute, and Co-Director of the Center for Innovative Study Design at the Stanford School of Medicine. He has held regular and visiting faculty appointments at Columbia University, UC Berkeley, and Nankai University, and holds advisory positions with the University of Hong Kong, Peking University, and Tsinghua University.

Howard Shek is a senior researcher at Tower Research Capital, where he has built and led the Core Research team with a mandate that covers the wide spectrum of research topics in automated trading. He has over 15 years of quantitative research and trading experience in fixed-income arbitrage, market microstructure, volatility estimation, option pricing, and portfolio theory, and has held senior trading and research positions at Merrill Lynch and J. P. Morgan, focusing