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Preface xiii

CHAPTER 1: FINANCIAL CRASHES: WHAT, HOW, WHY, AND WHEN? 3

What Are Crashes, and Why Do We Care? 3

The Crash of October 1987 5

Historical Crashes 7

The Tulip Mania 7

The South Sea Bubble 9

The Great Crash of October 1929 12

Extreme Events in Complex Systems 15

Is Prediction Possible? A Working Hypothesis 20

CHAPTER 2: FUNDAMENTALS OF FINANCIAL MARKETS 26

The Basics 27

Price Trajectories 27

Return Trajectories 30

Return Distributions and Return Correlation 33

The Ef .cient Market Hypothesis and the Random Walk 38

The Random Walk 38

A Parable: How Information Is Incorporated in Prices, Thus Destroying Potential "Free Lunches" 42

Prices Are Unpredictable, or Are They? 45

Risk-Return Trade-Off 47

CHAPTER 3: FINANCIAL CRASHES ARE "OUTLIERS" 49

What Are "Abnormal" Returns? 49

Drawdowns (Runs) 51

Definition of Drawdowns 51

Drawdowns and the Detection of "Outliers" 54

Expected Distribution of "Normal" Drawdowns 56

Drawdown Distributions of Stock Market Indices 60

The Dow Jones Industrial Average 60

The Nasdaq Composite Index 62

Further Tests 65

The Presence of Outliers Is a General Phenomenon 69

Main Stock Market Indices, Currencies, and Gold 70

Largest U.S. Companies 73

Synthesis 75

Symmetry-Breaking on Crash and Rally Days 76

Implications for Safety Regulations of Stock Markets 77

CHAPTER 4: POSITIVE FEEDBACKS 81

Feedbacks and Self-Organization in Economics 82

Hedging Derivatives, Insurance Portfolios, and Rational Panics 89

"Herd" Behavior and "Crowd" Effect 91

Behavioral Economics 91

Herding 94

Empirical Evidence of Financial Analysts 'Herding 96

Forces of Imitation 99

It Is Optimal to Imitate When Lacking Information 99

Mimetic Contagion and the Urn Models 104

Imitation from Evolutionary Psychology 106

Rumors 108

The Survival of the Fittest Idea 111

Gambling Spirits 112

"Anti-Imitation" and Self-Organization 114

Why It May Pay to Be in the Minority 114

El-Farol 's Bar Problem 115

Minority Games 117

Imitation versus Contrarian Behavior 118

Cooperative Behaviors Resulting from Imitation 121

The Ising Model of Cooperative Behavior 122

Complex Evolutionary Adaptive Systems of Boundedly Rational Agents 130

CHAPTER 5: MODELING FINANCIAL BUBBLES AND MARKET CRASHES 134

What Is a Model? 134

Strategy for Model Construction in Finance 135

Basic Principles 135

The Principle of Absence of Arbitrage Opportunity 136

Existence of Rational Agents 137

"Rational Bubbles" and Goldstone Modes of the Price "Parity Symmetry" Breaking 139

Price Parity Symmetry 140

Speculation as Spontaneous Symmetry Breaking 144

Basic Ingredients of the Two Models 148

The Risk-Driven Model 150

Summary of the Main Properties of the Model 150

The Crash Hazard Rate Drives the Market Price 152

Imitation and Herding Drive the Crash Hazard Rate 155

The Price-Driven Model 162

Imitation and Herding Drive the Market Price 162

The Price Return Drives the Crash Hazard Rate 164

Risk-Driven versus Price-Driven Models 168

CHAPTER 6: HIERARCHIES, COMPLEX FRACTAL DIMENSIONS, AND LOG-PERIODICITY 172

Critical Phenomena by Imitation on Hierarchical Networks 173

The Underlying Hierarchical Structure of Social Networks 173

Critical Behavior in Hierarchical Networks 177

A Hierarchical Model of Financial Bubbles 181

Origin of Log-Periodicity in Hierarchical Systems 186

Discrete Scale Invariance 186

Fractal Dimensions 188

Organization Scale by Scale: The Renormalization Group 192

Principle and Illustration of the Renormalization Group 192

The Fractal Weierstrass Function: A Singular Time-Dependent Solution of the Renormalization Group 195

Complex Fractal Dimensions and Log-Periodicity 198

Importance and Usefulness of Discrete Scale Invariance 208

Existence of Relevant Length Scales 208

Prediction 209

Scenarios Leading to Discrete Scale Invariance and Log-Periodicity 210

Newcomb-Benford Law of First Digits and the Arithmetic System 211

The Log-Periodic Law of the Evolution of Life? 213

Nonlinear Trend-Following versus Nonlinear Fundamental Analysis Dynamics 217

Trend Following: Positive Nonlinear Feedback and Finite-Time Singularity 218

Reversal to the Fundamental Value: Negative Nonlinear Feedback 220

Some Characteristics of the Price Dynamics of the Nonlinear Dynamical Model 223

CHAPTER 7: AUTOPSY OF MAJOR CRASHES: UNIVERSAL EXPONENTS AND LOG-PERIODICITY 228

The Crash of October 1987 228

Precursory Pattern 231

Aftershock Patterns 236

The Crash of October 1929 239

The Three Hong Kong Crashes of 1987, 1994, and 1997 242

The Hong Kong Crashes 242

The Crash of October 1997 and Its Resonance on the U.S. Market 246

Currency Crashes 254

The Crash of August 1998 259

Nonparametric Test of Log-Periodicity 263

The Slow Crash of 1962 Ending the "Tronics" Boom 266

The Nasdaq Crash of April 2000 269

"Antibubbles" 275

The "Bearish" Regime on the Nikkei Starting from January 1, 1990 276

The Gold Deflation Price Starting in Mid-1980 278

Synthesis:"Emergent "Behavior of the Stock Market 279

CHAPTER 8: BUBBLES, CRISES, AND CRASHES IN EMERGENT MARKETS 281

Speculative Bubbles in Emerging Markets 281

Methodology 285

Latin-American Markets 286

Asian Markets 295

The Russian Stock Market 304

Correlations across Markets: Economic Contagion and Synchronization of Bubble Collapse 309

Implications for Mitigations of Crises 314

CHAPTER 9: PREDICTION OF BUBBLES, CRASHES, AND ANTIBUBBLES 320

The Nature of Predictions 320

How t Develop and Interpret Statistical Tests of Log-Periodicity 325

First Guidelines for Prediction 329

What Is the Predictive Power of Equation (15)? 329

How Long Prior to a Crash Can One Identify the Log-Periodic

Signatures? 330

A Hierarchy f Prediction Schemes 334

The Simple Power Law 334

The "Linear" Log-Periodic Formula 335

The "Nonlinear" Log-Periodic Formula 336

The Shank 's Transformation on a Hierarchy of Characteristic Times 336

Application to the October 1929 Crash 337

Application to the October 1987 Crash 338

Forward Predictions 338

Successful Prediction of the Nikkei 1999 Antibubble 339

Successful Prediction of the Nasdaq Crash of April 2000 342

The U.S. Market, December 1997 False Alarm 342

The U.S.Market, October 1999 False Alarm 346

Present Status of Forward Predictions 346

The Finite Probability That No Crash Will Occur during a Bubble 346

Estimation of the Statistical Significance of the Forward Predictions 347

Statistical Confidence of the Crash "Roulette" 347

Statistical Significance of a Single Successful Prediction via Bayes's Theorem 349

The Error Diagram and the Decision Process 351

Practical Implications on Different Trading Strategies 352

CHAPTER 10: 2050: THE END OF THE GROWTH ERA? 355

Stock Markets, Economics, and Population 355

The Pessimistic Viewpoint of "Natural" Scientists 357

The Optimistic Viewpoint of "Social" Scientists 359

Analysis of the Faster-Than-Exponential Growthof Population, GDP, and Financial Indices 361

Refinements of the Analysis 369

Complex Power Law Singularities 369

Prediction for the Coming Decade 371

The Aging "Baby Boomers" 377

Related Works and Evidence 378

Scenarios for the "Singularity" 383

Collapse 384

Transition to Sustainability 389

Resuming Accelerating Growth by Overpassing Fundamental Barriers 393

The Increasing Propensity to Emulate the Stock Market Approach 395

References 397

Index 419

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