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Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications

Francois Longin (Editor)
ISBN: 978-1-118-65019-6
640 pages
October 2016
Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications (1118650190) cover image

Description

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.

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Table of Contents

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 187

8.7 Conclusion 192

References 192

9 Statistics of Extremes: Challenges and Opportunities 195
M. de Carvalho

9.1 Introduction 195

9.2 Statistics of bivariate extremes 196

9.3 Models based on families of tilted measures 204

9.4 Miscellanea 209

References 211

10 Measures of Financial Risk 215
S.Y. Novak

10.1 Introduction 215

10.2 Traditional measures of risk 215

10.3 Risk estimation 218

10.4 “Technical analysis” of financial data 222

10.5 Dynamic risk measurement 226

10.6 Open problems and further research 234

10.7 Conclusion 235

Acknowledgment 235

References 235

11 On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures 239
Marie Kratz

11.1 Introduction 239

11.2 A brief review of existing methods 245

11.3 New approaches: Mixed limit theorems 247

11.4 Application to risk measures and comparison 269

11.5 Conclusion 277

References 279

12 Estimation Methods for Value at Risk 283
Saralees Nadarajah and Stephen Chan

12.1 Introduction 283

12.2 General properties 289

12.3 Parametric methods 300

12.4 Nonparametric methods 326

12.5 Semiparametric methods 332

12.6 Computer software 344

12.7 Conclusions 347

Acknowledgment 347

References 347

13 Comparing Tail Risk and Systemic Risk Profiles for Different Types of U.S. Financial Institutions 357
Stefan Straetmans and Thanh Thi Huyen Dinh

13.1 Introduction 357

13.2 Tail risk and systemic risk indicators 361

13.3 Tail risk and systemic risk estimation 364

13.4 Empirical results 368

13.5 Conclusions 381

References 382

14 Extreme Value Theory and Credit Spreads 391
Wesley Phoa

14.1 Preliminaries 391

14.2 Tail behavior of credit markets 394

14.3 Some multivariate analysis 398

14.4 Approximating value at risk for credit portfolios 401

14.5 Other directions 403

References 404

15 Extreme Value Theory and Risk Management in Electricity Markets 405
Kam Fong Chan and Philip Gray

15.1 Introduction 405

15.2 Prior literature 407

15.3 Specification of VaR estimation approaches 409

15.4 Empirical analysis 413

15.5 Conclusion 422

Acknowledgment 423

References 423

16 Margin Setting and Extreme Value Theory 427
John Cotter and Kevin Dowd

16.1 Introduction 427

16.2 Margin setting 428

16.3 Theory and methods 430

16.4 Empirical results 434

16.5 Conclusions 439

Acknowledgment 440

References 440

17 The Sortino Ratio and Extreme Value Theory: An Application to Asset Allocation 443
G. Geoffrey Booth and John Paul Broussard

17.1 Introduction 443

17.2 Data definitions and description 446

17.3 Performance ratios and their estimations 451

17.4 Performance measurement results and implications 456

17.5 Concluding remarks 460

Acknowledgments 461

References 461

18 Portfolio Insurance: The Extreme Value Approach Applied to the CPPI Method 465
Philippe Bertrand and Jean-Luc Prigent

18.1 Introduction 465

18.2 The CPPI method 467

18.3 CPPI and quantile hedging 472

18.4 Conclusion 481

References 481

19 The Choice of the Distribution of Asset Returns: How Extreme Value Can Help? 483
François Longin

19.1 Introduction 483

19.2 Extreme value theory 485

19.3 Estimation of the tail index 488

19.4 Application of extreme value theory to discriminate among distributions of returns 490

19.5 Empirical results 493

19.6 Conclusion 501

References 501

20 Protecting Assets Under Non-Parametric Market Conditions 507
Jean-Marie Choffray and Charles Pahud de Mortanges

20.1 Investors’ “known knowns” 509

20.2 Investors’ “known unknowns” 512

20.3 Investors’ “unknown knowns” 515

20.4 Investors’ “unknown unknowns” 518

20.5 Synthesis 522

References 523

21 EVT Seen by a Vet: A Practitioner’s Experience on Extreme Value Theory 525
Jean-François Boulier

21.1 What has the vet done? 525

21.2 Why use EVT? 526

21.3 What EVT could additionally bring to the party? 528

21.4 A final thought 528

References 528

22 The Robotization of Financial Activities: A Cybernetic Perspective 529
Hubert Rodarie

22.1 An increasingly complex system 530

22.2 Human error 532

22.3 Concretely, what do we need to do to transform a company into a machine? 534

References 543

23 Two Tales of Liquidity Stress 545
Jacques Ninet

23.1 The french money market fund industry. How history has shaped a potentially vulnerable framework 546

23.2 The 1992–1995 forex crisis 547

23.3 Four mutations paving the way for another meltdown 549

23.4 The subprime crisis spillover. How some MMFs were forced to lock and some others not 551

23.5 Conclusion. What lessons can be drawn from these two tales? 552

Further Readings 553

24 Managing Operational Risk in the Banking Business – An Internal Auditor Point of View 555
Maxime Laot

Further Reading 559

References 560

Annexes 560

25 Credo Ut Intelligam 563
Henri Bourguinat and Eric Briys

25.1 Introduction 563

25.2 “Anselmist” finance 563

25.3 Casino or dance hall? 565

25.4 Simple-minded diversification 566

25.5 Homo sapiens versus homo economicus 568

Acknowledgement 569

References 569

26 Bounded Rationalities, Routines, and Practical as well as Theoretical Blindness: On the Discrepancy Between Markets and Corporations 571
Laurent Bibard

26.1 Introduction: Expecting the unexpected 571

26.2 Markets and corporations: A structural and self-disruptive divergence of interests 572

26.3 Making a step back from a dream: On people expectations 574

26.4 How to disentangle people from a unilateral short-term orientation? 578

References 580

Name Index 583

Subject Index 593

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