Extreme Events in Finance

François Longin, PhD, is Professor in the Department of Finance at ESSEC Business School, France. He has been working on the applications of extreme value theory to financial markets for many years, and his research has been applied by financial institutions in the risk management area including market, credit, and operational risks. His research works can be found in scientific journals such as The Journal of Finance. Dr. Longin is currently a financial consultant with expertise covering risk management for financial institutions and portfolio management for asset management firms.

A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector
 
Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions.
 
Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes:
 
* Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk management
 
* Topical discussions on univariate and multivariate case extremes as well as regulation in financial markets
 
* Extensive references in order to provide readers with resources for further study
 
* Discussions on using R packages to compute the value of risk and related quantities
 
The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance.
 
François Longin, PhD, is Professor in the Department of Finance at ESSEC Business School, France. He has been working on the applications of extreme value theory to financial markets for many years, and his research has been applied by financial institutions in the risk management area including market, credit, and operational risks. His research works can be found in scientific journals such as The Journal of Finance. Dr. Longin is currently a financial consultant with expertise covering risk management for financial institutions and portfolio management for asset management firms.

About the Editor xiii
 
About the Contributors xv
 
1 Introduction 1
François Longin
 
1.1 Extremes 1
 
1.2 History 2
 
1.3 Extreme value theory 2
 
1.4 Statistical estimation of extremes 2
 
1.5 Applications in finance 4
 
1.6 Practitioners' points of view 6
 
1.7 A broader view on modeling extremes 6
 
1.8 Final words 7
 
1.9 Thank you note 7
 
References 8
 
2 Extremes Under Dependence--Historical Development and Parallels with Central Limit Theory 11
M.R. Leadbetter
 
2.1 Introduction 11
 
2.2 Classical (I.I.D.) central limit and extreme value theories 12
 
2.3 Exceedances of levels, kth largest values 14
 
2.4 CLT and EVT for stationary sequences, bernstein's blocks, and strong mixing 15
 
2.5 Weak distributional mixing for EVT, D(un), extremal index 18
 
2.6 Point process of level exceedances 19
 
2.7 Continuous parameter extremes 20
 
References 22
 
3 The Extreme Value Problem in Finance: Comparing the Pragmatic Program with the Mandelbrot Program 25
Christian Walter
 
3.1 The extreme value puzzle in financial modeling 25
 
3.2 The sato classification and the two programs 28
 
3.3 Mandelbrot's program: A fractal approach 34
 
3.4 The Pragmatic Program: A data-driven approach 39
 
3.5 Conclusion 47
 
Acknowledgments 48
 
References 48
 
4 Extreme Value Theory: An Introductory Overview 53
Isabel Fraga Alves and Cláudia Neves
 
4.1 Introduction 53
 
4.2 Univariate case 56
 
4.3 Multivariate case: Some highlights 84
 
Further reading 90
 
Acknowledgments 90
 
References 90
 
5 Estimation of the Extreme Value Index 97
Beirlant J., Herrmann K., and Teugels J.L.
 
5.1 Introduction 97
 
5.2 The main limit theorem behind extreme value theory 98
 
5.3 Characterizations of the max-domains of attraction and extreme value index estimators 99
 
5.4 Consistency and asymptotic normality of the estimators 103
 
5.5 Second-order reduced-bias estimation 104
 
5.6 Case study 106
 
5.7 Other topics and comments 108
 
References 111
 
6 Bootstrap Methods in Statistics of Extremes 117
M. Ivette Gomes, Frederico Caeiro, Lígia Henriques-Rodrigues, and B.G. Manjunath
 
6.1 Introduction 117
 
6.2 A few details on EVT 119
 
6.3 The bootstrap methodology in statistics of univariate extremes 127
 
6.4 Applications to simulated data 133
 
6.5 Concluding remarks 133
 
Acknowledgments 135
 
References 135
 
7 Extreme Values Statistics for Markov Chains with Applications to Finance and Insurance 139
Patrice Bertail, Stéphan Clémençon, and Charles Tillier
 
7.1 Introduction 139
 
7.2 On the (pseudo) regenerative approach for markovian data 141
 
7.3 Preliminary results 151
 
7.4 Regeneration-based statistical methods for extremal events 154
 
7.5 The extremal index 156
 
7.6 The regeneration-based hill estimator 159
 
7.7 Applications to ruin theory and financial time series 161
 
7.8 An application to the CAC40 165
 
7.9 Conclusion 167
 
References 167
 
8 Lévy Processes and Extreme Value Theory 171
Olivier Le Courtois and Christian Walter
 
8.1 Introduction 171
 
8.2 Extreme value theory 173
 
8.3 Infinite divisibility and Lévy processes 178
 
8.4 Heavy-tailed Lévy processes 182
 
8.5 Semi-heavy-tailed Lévy processes 184
 
8.6 Lévy processes and extreme values 1