SUMMARY

• Provides a comprehensive overview of extreme value theory from a financial perspective

• Expert academics examine the recent developments in the modelling of extreme events

• Offers an extension of traditional VAR methodologies and provides analysis of abnormal distribution at the end of the curve

• Examines the patterns and likelihood of the occurrence of extreme events

• Contributions selected and introduced by the leading academic in the field, Paul Embrechts of Federal Institute of Technology (ETH), Zurich

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  TABLE OF CONTENTS

CONTENTS
Introduction
Paul Embrechts
and
The Bell Curve is Wrong: So What
Paul Embrechts

BASIC EXTREME VALUE THEORY

1 Extreme Value Theory for Risk Managers
Alexander J. McNeil
2 Measuring Risk with Extreme Value Theory
Richard L. Smith
3 Adaptive Threshold Selection in Tail Index Estimation
Jan Beirlant and Gunther Matthys
4 Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management
Francis X. Diebold, Til Schuermann and John D. Stroughair
5 Modelling Multivariate Extremes
Paul Embrechts, Laurens de Haan and Xin Huang

RISK MEASURES AND EXTREME VALUE THEORY

6 Correlation: Pitfalls and Alternatives
Paul Embrechts, Alex McNeil and Daniel Straumann
7 Thinking Coherently
Philippe Artzner, Freddy Delbaen, Jean-Marc Eber and David Heath

APPLICATIONS TO FINANCE

8 Value-at-Risk and Extreme Returns
Jon Danielsson and Casper G. de Vries
9 Reading the Riskometer
Alexander J. McNeil
10 Extreme Value Theory: An Empirical Analysis of Equity Risk
John Gavin
11 From Value at Risk to Stress Testing: the Extreme Value Approach
François M. Longin
12 Is it Really Long Memory We See in Financial Returns?
Catalin Starica and Thomas Mikosch
13 Multivariate Extremes for Foreign Exchange Data
Catalin Starica
14 Spill-overs in Financial Markets
Stefan Straetmans
15 Modelling and Measuring Operational Risk
Marcelo Cruz, Rodney Coleman and Gerry Salkin

APPLICATIONS TO INSURANCE

16 Extreme Value Statistics and Wind Storm Losses: A Case Study
Holger Rootzén and Nader Tajvidi
17 Bayesian Risk Analysis
Richard L. Smith and Dougal Goodman
18 Developing Scenarios for Future Extreme Losses Using the POT Method
Alexander J. McNeil and Thomas Saladin

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  QUOTES

"Timely, well organised and up-to-date...this book is a must for all risk managers."
Daniel M. Dumas de Rauly, BNP Paribas Group

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  REVIEW

Daniel M. Dumas de Rauly, BNP-PARIBAS Group
In the wake of a string of highly-publicized cases, Barings or LTCM to name a few, and recent financial crises, in 1994 or 1998 for instance, risk managers have been made aware that extreme losses occur more often than their models tell them they should. With respect to a given loss distribution, one can summarize in stating that existing risk models tend to exhibit a good fit in its central part while they do a very poor and dangerous job in its tails since the more extreme the level of loss chosen, the more underestimated is the probability that such a loss would happen.

Beyond that simple but potentially dangerous situation that is in itself a dramatic example of model risk if not of human hubris, those same risk managers have now identified the culprit, i.e. the ever-present underlying assumption in their models that the world of losses is a 'normal' world or, in the words of Paul Embrechts, a world of normal thinking.

Edited by Paul Embrechts, Extremes and Integrated Risk Management delivers an overall message of hope : in the quest for a better world of risk management, more specifically for risk models that would allow an acceptable assessment of both probability of occurrence and size of very high financial losses, there is an already well-developed tool known as 'Extreme Value Theory' or EVT, an offshoot from the probability theory that offers adequate solutions since it focuses explicitly on extreme innovations, but poses also new challenges to the financial engineers in charge of risk analytics.

Stemming from 'normal' thinking embedded in existing risk models, two major pitfalls have emerged : first, a definite propensity to properly handle most of the recorded losses -losses that are frequent and not extreme- at the expense of the very rare but extreme losses and second, an inability to address stress-testing without which, in my opinion, there is no good framework for a risk management system. If the first one is especially important for credit risk analytics, the second is no less important for market risk analytics to which the idea already submitted in a previous article from RISK applies best, that a process generating normal daily returns is not necessarily inconsistent with occasional crashes .

This book shows how EVT helps to overcome these pitfalls and to what extent it does succeed in doing so. While on the one hand I somewhat regret that its emphasis is much more on tail-fitting than on stress-testing or, in technical terms, more on peaks-over-threshold models than on block maxima models, on the other hand I wish to underline that most recent developments about such important issues as selecting optimal thresholds, estimating tail parameters or modelling multivariate extremes, are presented in a manner that is both consistent and readable by most risk managers.

At the very onset of this book's second section lies a true gem, the article Correlation : pitfalls and alternatives. Not only does it show how fallacious the often-heard statement is according to which correlation is the tool for dependence measurement, but with the concept of copula functions it also brings an answer to the modelling issue of dependent risks.

With respect to the third section of this work, more specifically to applications of EVT in finance, I found regrettable the absence of articles already published on using EVT for credit risk analytics. This is rather surprising since I am of the opinion that this is where tail-fitting procedures from peaks-over-threshold models shine. Moreover, had such reprints been added, it would have opened the door to the concept of credit VaR and consequently to economic capital. As a matter of fact, with the one exception of a reprint referring to operational risk, chosen applications pertain only to using EVT for market risk analytics while, contrasting with that, stress-testing procedures using block maxima models that are according to me quite important for market risk management are not really addressed.

This being said, through his choice of reprinted articles Paul Embrechts has in my opinion succeeded with respect to his main objective of striking a balance between theory and applications in finance and insurance. There is no doubt that this book is timely, well-organized, up-to-date and that it covers a lot of issues.

I would even venture to say that risk managers today who do not know anything about EVT fail to carry out a very important part of the job they are paid for. Since one can say that they are only as good as their risk assessment of future situations and their suggestions for risk reduction, what would shareholders think if they were only able to characterize average outcomes but not extreme outcomes, i.e. those characterized by low probabilities of occurrence and high amounts of money at stake ? Let us not forget that the very existence of financial firms is only threatened by the latter.

Leaving aside the highly mathematical aspects of EVT while succeeding in exposing its essence, this book is a must for risk managers. As a bare minimum, I strongly recommend that they read and give some thought to Paul Embrechts's message in his piece entitled The bell curve is wrong : so what ?

1 In other words, the empirical distribution of losses over time may be fitted with a normal or gaussian distribution depicted by the well-known bell curve.
2 EVT dates back to the 1920s and has been around in casualty insurance for many years.
3 History Repeating from Alexander McNeil, RISK (January 1998).

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  CONTRIBUTORS

Alexander J. McNeil, Richard L. Smith, Jan Beirlant, Gunther Matthys, Francis X. Diebold, Til Schuermann, John D. Stroughair, Laurens de Haan, Xin Huang, Daniel Straumann, Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, David Heath, Jon Danielsson, Casper G. de Vries, John Gavin, François M. Longin, Catalin Starica, Thomas Mikosch, Stefan Straetmans, Marcelo Cruz, Rodney Coleman,Gerry Salkin, Holger Rootzén, Nader Tajvidi, Richard L. Smith, Dougal Goodman, Thomas Saladin
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