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CHAPTER 1
Monte Carlo or Bust 1
Beginning 1
Whither? And Allusions 4
CHAPTER 2
Statistical Arbitrage 9
Introduction 9
Noise Models 10
Reverse Bets 11
Multiple Bets 11
Rule Calibration 12
Spread Margins for Trade Rules 16
Popcorn Process 18
Identifying Pairs 20
Refining Pair Selection 21
Event Analysis 22
Correlation Search in the Twenty-First Century 26
Portfolio Configuration and Risk Control 26
Exposure to Market Factors 29
Market Impact 30
Risk Control Using Event Correlations 31
Dynamics and Calibration 32
Evolutionary Operation: Single Parameter Illustration 34
CHAPTER 3
Structural Models 37
Introduction 37
Formal Forecast Functions 39
Exponentially Weighted Moving Average 40
Classical Time Series Models 47
Autoregression and Cointegration 47
Dynamic Linear Model 49
Volatility Modeling 50
Pattern Finding Techniques 51
Fractal Analysis 52
Which Return? 52
A Factor Model 53
Factor Analysis 54
Defactored Returns 55
Prediction Model 57
Stochastic Resonance 58
Practical Matters 59
Doubling: A Deeper Perspective 61
Factor Analysis Primer 63
Prediction Model for Defactored Returns 65
CHAPTER 4
Law of Reversion 67
Introduction 67
Model and Result 68
The 75 percent Rule 68
Proof of the 75 percent Rule 69
Analytic Proof of the 75 percent Rule 71
Discrete Counter 73
Generalizations 73
Inhomogeneous Variances 74
Volatility Bursts 75
Numerical Illustration 76
First-Order Serial Correlation 77
Analytic Proof 79
Examples 82
Nonconstant Distributions 82
Applicability of the Result 84
Application to U.S. Bond Futures 85
Summary 87
Appendix 4.1: Looking Several Days Ahead 87
CHAPTER 5
Gauss Is Not the God of Reversion 91
Introduction 91
Camels and Dromedaries 92
Dry River Flow 95
Some Bells Clang 98
CHAPTER 6
Interstock Volatility 99
Introduction 99
Theoretical Explanation 103
Theory versus Practice 105
Finish the Theory 105
Finish the Examples 106
Primer on Measuring Spread Volatility 108
CHAPTER 7
Quantifying Reversion Opportunities 113
Introduction 113
Reversion in a Stationary Random Process 114
Frequency of Reversionary Moves 117
Amount of Reversion 118
Movements from Quantiles Other Than
the Median 135
Nonstationary Processes: Inhomogeneous Variance 136
Sequentially Structured Variances 136
Sequentially Unstructured Variances 137
Serial Correlation 138
Appendix 7.1: Details of the Lognormal Case in Example 6 139
CHAPTER 8
Nobel Difficulties 141
Introduction 141
Event Risk 142
Will Narrowing Spreads Guarantee Profits? 144
Rise of a New Risk Factor 145
Redemption Tension 148
Supercharged Destruction 150
The Story of Regulation Fair Disclosure (FD) 150
Correlation During Loss Episodes 151
CHAPTER 9
Trinity Troubles 155
Introduction 155
Decimalization 156
European Experience 157
Advocating the Devil 158
Stat. Arb. Arbed Away 159
Competition 160
Institutional Investors 163
Volatility Is the Key 163
Interest Rates and Volatility 165
Temporal Considerations 166
Truth in Fiction 174
A Litany of Bad Behavior 174
A Perspective on 2003 178
Realities of Structural Change 179
Recap 180
CHAPTER 10
Arise Black Boxes 183
Introduction 183
Modeling Expected Transaction Volume and Market Impact 185
Dynamic Updating 188
More Black Boxes 189
Market Deflation 189
CHAPTER 11
Statistical Arbitrage Rising 191
Catastrophe Process 194
Catastrophic Forecasts 198
Trend Change Identification 200
Using the Cuscore to Identify a Catastrophe 202
Is It Over? 204
Catastrophe Theoretic Interpretation 205
Implications for Risk Management 209
Sign Off 211
Appendix 11.1: Understanding the Cuscore 211
Bibliography 223
Index 225
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