لایب سان

Author(s): Zhaodong Wang, Weian Zheng

Series: East China Normal University Scientific Reports

Publisher: World Scientific Publishing Company, Year: 2014

ISBN: 9814616508,9789814616508

Foreword ix Preface xi About the Authors xiii 1. Introduction 1 2. Market Microstructure 7 2.1 Trading Products . . . . . . . . . . . . . . . . . . . 7 2.2 Trading Model . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Continuous Trading . . . . . . . . . . . . . 12 2.2.2 Auction . . . . . . . . . . . . . . . . . . . . 15 2.3 Market Data Information . . . . . . . . . . . . . . 21 2.4 Trading Interface . . . . . . . . . . . . . . . . . . . 24 2.5 Risk Control . . . . . . . . . . . . . . . . . . . . . 29 2.6 Transaction Costs . . . . . . . . . . . . . . . . . . 35 2.7 Differences with Western Market . . . . . . . . . . 35 3. Some Basic HFT Strategies 37 3.1 General . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Arbitrage . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 Definition of Arbitrage . . . . . . . . . . . . 38 3.2.2 Different Types of Arbitrage . . . . . . . . . 40 3.2.3 Process of Arbitrage . . . . . . . . . . . . . 43 3.3 Ticker Tape Trading . . . . . . . . . . . . . . . . . 49 3.4 Market Making . . . . . . . . . . . . . . . . . . . . 52 v August 14, 2014 10:16 High-Frequency Trading and Probability Theory - 9in x 6in b1829-fm page vi vi Contents 3.5 Event Driven . . . . . . . . . . . . . . . . . . . . . 54 3.6 Other Basic Strategies . . . . . . . . . . . . . . . . 56 4. IT System 59 4.1 Challenges . . . . . . . . . . . . . . . . . . . . . . 59 4.2 Trading System Design . . . . . . . . . . . . . . . 61 4.2.1 Trading Interface . . . . . . . . . . . . . . . 62 4.2.2 Trading Process Control . . . . . . . . . . . 66 4.2.3 Risk Control and Surveillance . . . . . . . . 70 4.2.4 Strategy Implementation . . . . . . . . . . . 75 4.2.5 Monitoring . . . . . . . . . . . . . . . . . . 77 4.3 Environment . . . . . . . . . . . . . . . . . . . . . 77 4.3.1 Programming Language . . . . . . . . . . . 77 4.3.2 Server and Operation System Selection . . . 78 4.3.3 Network Environment . . . . . . . . . . . . 79 4.4 Core Technologies . . . . . . . . . . . . . . . . . . 81 4.4.1 Single-Process vs. Multi-Process . . . . . . . 81 4.4.2 Code Optimization . . . . . . . . . . . . . . 82 4.4.3 Memory Management . . . . . . . . . . . . 83 4.4.4 Managing CPU Cache . . . . . . . . . . . . 83 5. Stationary Process and Ergodicity 85 5.1 Some Basics of Probability Theory . . . . . . . . . 85 5.1.1 Probability Space . . . . . . . . . . . . . . . 86 5.1.2 Random Variables . . . . . . . . . . . . . . 88 5.1.3 Conditional Probability . . . . . . . . . . . . 89 5.1.4 Two Main Theorems . . . . . . . . . . . . . 90 5.1.4.1 The strong law of large number . . . 91 5.1.4.2 The central limit theorem . . . . . . 92 5.2 Stochastic Process . . . . . . . . . . . . . . . . . . 92 5.2.1 Examples of Stochastic Processes . . . . . . 92 5.2.2 Stationary Process and Ergodic Theory . . . 93 5.2.2.1 The strong ergodic theorem . . . . . 95 5.2.3 Testing Stationarity . . . . . . . . . . . . . . 97 5.2.4 Semi-Martingales and Filtering Problem . . . 98 5.2.5 Stationary Process as Noises . . . . . . . . . 100 August 14, 2014 10:16 High-Frequency Trading and Probability Theory - 9in x 6in b1829-fm page vii Contents vii 5.3 Time Series Analysis . . . . . . . . . . . . . . . . . 101 5.4 Pair-Trading Revisited . . . . . . . . . . . . . . . . 104 6. Stationarity and Technical Analysis 109 6.1 Technical Analysis . . . . . . . . . . . . . . . . . . 111 6.2 Logarithmic Return is Stationary . . . . . . . . . . 113 6.3 Moving Average and Exponential Moving Average . . . . . . . . . . . . . . . . . . . 115 6.4 Bollinger Bands . . . . . . . . . . . . . . . . . . . 120 6.5 Moving Average Convergence–Divergence . . . . . 123 6.6 Rate of Change . . . . . . . . . . . . . . . . . . . . 126 6.7 Relative Strength Index . . . . . . . . . . . . . . . 127 6.8 Stochastic Oscillators . . . . . . . . . . . . . . . . 129 6.9 Directional Movement Index . . . . . . . . . . . . 133 6.10 Parabolic SAR . . . . . . . . . . . . . . . . . . . . 138 7. HFT of a Single Asset 141 7.1 Stochastic Integral of Stationary Processes . . . . . 142 7.1.1 Ito-Riemann Sums and Their Limit . . . . . 142 7.1.2 Profit of HFT and Strong Ergodic Theorem . . . . . . . . . . . . . . . 143 7.1.3 Sharpe Ratio Test for HFT . . . . . . . . . . 147 7.2 Two Examples . . . . . . . . . . . . . . . . . . . . 149 7.2.1 The First Example . . . . . . . . . . . . . . 149 7.2.2 The Second Example . . . . . . . . . . . . . 151 8. Bid, Ask and Trade Prices 155 9. Financial Engineering 15

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