| On the Origin of Risks and Extremes | p. 1 |
| The Multidimensional Nature of Risk and Dependence | p. 1 |
| How to Rank Risks Coherently? | p. 4 |
| Coherent Measures of Risks | p. 4 |
| Consistent Measures of Risks and Deviation Measures | p. 7 |
| Examples of Consistent Measures of Risk | p. 10 |
| Origin of Risk and Dependence | p. 13 |
| The CAPM View | p. 13 |
| The Arbitrage Pricing Theory (APT) and the Fama-French Factor Model | p. 18 |
| The Efficient Market Hypothesis | p. 20 |
| Emergence of Dependence Structures in the Stock Markets | p. 24 |
| Large Risks in Complex Systems | p. 29 |
| Appendix | p. 30 |
| Why Do Higher Moments Allow us to Assess Larger Risks? | p. 30 |
| Marginal Distributions of Returns | p. 33 |
| Motivations | p. 33 |
| A Brief History of Return Distributions | p. 37 |
| The Gaussian Paradigm | p. 37 |
| Mechanisms for Power Laws in Finance | p. 39 |
| Empirical Search for Power Law Tails and Possible Alternatives | p. 42 |
| Constraints from Extreme Value Theory | p. 43 |
| Main Theoretical Results on Extreme Value Theory | p. 45 |
| Estimation of the Form Parameter and Slow Convergence to Limit Generalized Extreme Value (GEV) and Generalized Pareto (GPD) Distributions | p. 47 |
| Can Long Memory Processes Lead to Misleading Measures of Extreme Properties? | p. 51 |
| GEV and GPD Estimators of the Distributions of Returns of the Dow Jones and Nasdaq Indices | p. 52 |
| Fitting Distributions of Returns with Parametric Densities | p. 54 |
| Definition of Two Parametric Families | p. 54 |
| Parameter Estimation Using Maximum Likelihood and Anderson-Darling Distance | p. 60 |
| Empirical Results on the Goodness-of-Fits | p. 62 |
| Comparison of the Descriptive Power of the Different Families | p. 69 |
| Discussion and Conclusions | p. 76 |
| Summary | p. 76 |
| Is There a Best Model of Tails? | p. 76 |
| Implications for Risk Assessment | p. 78 |
| Appendix | p. 80 |
| Definition and Main Properties of Multifractal Processes | p. 80 |
| A Survey of the Properties of Maximum Likelihood Estimators | p. 87 |
| Asymptotic Variance-Covariance of Maximum Likelihood Estimators of the SE Parameters | p. 91 |
| Testing the Pareto Model versus the Stretched-Exponential Model | p. 93 |
| Notions of Copulas | p. 99 |
| What is Dependence? | p. 101 |
| Definition and Main Properties of Copulas | p. 103 |
| A Few Copula Families | p. 107 |
| Elliptical Copulas | p. 107 |
| Archimedean Copulas | p. 111 |
| Extreme Value Copulas | p. 116 |
| Universal Bounds for Functionals of Dependent Random Variables | p. 118 |
| Simulation of Dependent Data with a Prescribed Copula | p. 120 |
| Simulation of Random Variables Characterized by Elliptical Copulas | p. 120 |
| Simulation of Random Variables Characterized by Smooth Copulas | p. 122 |
| Application of Copulas | p. 124 |
| Assessing Tail Risk | p. 124 |
| Asymptotic Expression of the Value-at-Risk | p. 128 |
| Options on a Basket of Assets | p. 131 |
| Basic Modeling of Dependent Default Risks | p. 137 |
| Appendix | p. 138 |
| Simple Proof of a Theorem on Universal Bounds for Functionals of Dependent Random Variables | p. 138 |
| Sketch of a Proof of a Large Deviation Theorem for Portfolios Made of Weibull Random Variables | p. 140 |
| Relation Between the Objective and the Risk-Neutral Copula | p. 143 |
| Measures of Dependences | p. 147 |
| Linear Correlations | p. 147 |
| Correlation Between Two Random Variables | p. 147 |
| Local Correlation | p. 151 |
| Generalized Correlations Between N > 2 Random Variables | p. 152 |
| Concordance Measures | p. 154 |
| Kendall's Tau | p. 154 |
| Measures of Similarity Between Two Copulas | p. 158 |
| Common Properties of Kendall's Tau, Spearman's Rho and Gini's Gamma | p. 161 |
| Dependence Metric | p. 162 |
| Quadrant and Orthant Dependence | p. 164 |
| Tail Dependence | p. 168 |
| Definition | p. 168 |
| Meaning and Refinement of Asymptotic Independence | p. 168 |
| Tail Dependence for Several Usual Models | p. 170 |
| Practical Implications | p. 177 |
| Appendix | p. 182 |
| Tail Dependence Generated by Student's Factor Model | p. 182 |
| Description of Financial Dependences with Copulas | p. 189 |
| Estimation of Copulas | p. 190 |
| Nonparametric Estimation | p. 190 |
| Semiparametric Estimation | p. 195 |
| Parametric Estimation | p. 200 |
| Goodness-of-Fit Tests | p. 203 |
| Description of Financial Data in Terms of Gaussian Copulas | p. 204 |
| Test Statistics and Testing Procedure | p. 204 |
| Empirical Results | p. 207 |
| Limits of the Description in Terms of the Gaussian Copula | p. 212 |
| Limits of the Tests | p. 212 |
| Sensitivity of the Method | p. 213 |
| The Student Copula: An Alternative? | p. 215 |
| Accounting for Heteroscedasticity | p. 217 |
| Summary | p. 219 |
| Appendix | p. 221 |
| Proof of the Existence of a X[superscript 2]-Statistic for Testing Gaussian Copulas | p. 221 |
| Hypothesis Testing with Pseudo Likelihood | p. 222 |
| Measuring Extreme Dependences | p. 227 |
| Motivations | p. 230 |
| Suggestive Historical Examples | p. 230 |
| Review of Different Perspectives | p. 231 |
| Conditional Correlation Coefficient | p. 233 |
| Definition | p. 234 |
| Influence of the Conditioning Set | p. 234 |
| Influence of the Underlying Distribution for a Given Conditioning Set | p. 237 |
| Conditional Correlation Coefficient on Both Variables | p. 239 |
| An Example of Empirical Implementation | p. 240 |
| Summary | p. 246 |
| Conditional Concordance Measures | p. 247 |
| Definition | p. 248 |
| Example | p. 249 |
| Empirical Evidence | p. 251 |
| Extreme Co-movements | p. 254 |
| Synthesis and Consequences | p. 256 |
| Appendix | p. 261 |
| Correlation Coefficient for Gaussian Variables Conditioned on Both X and Y Larger Than u | p. 261 |
| Conditional Correlation Coefficient for Student's Variables | p. 266 |
| Conditional Spearman's Rho | p. 270 |
| Summary and Outlook | p. 271 |
| Synthesis | p. 271 |
| Outlook and Future Directions | p. 274 |
| Robust and Adaptive Estimation of Dependences | p. 274 |
| Outliers, Kings, Black Swans and Their Dependence | p. 276 |
| Endogeneity Versus Exogeneity | p. 276 |
| Nonstationarity and Regime Switching in Dependence | p. 279 |
| Time-Varying Lagged Dependence | p. 280 |
| Toward a Dynamical Microfoundation of Dependences | p. 281 |
| References | p. 283 |
| Index | p. 309 |
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