(2002). An Introduction to Statistical Modeling of Extreme Values. Technometrics: Vol. 44, No. 4, pp. 397-397.

An Introduction to Statistical Modeling of Extreme Values

(2002). Modelling Extremal Events for Insurance and Finance. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 360-360.

Modelling Extremal Events for Insurance and Finance

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Quantitative Risk Management: Concepts, Techniques, and Tools

An overview of model-based geostatistics.- Gaussian models for geostatistical data.- Generalized linear models for geostatistical data.- Classical parameter estimation.- Spatial prediction.- Bayesian inference.- Geostatistical design.

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Model-based Geostatistics

Non-Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.

Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics

1. Introduction.- 2. Basics of Statistical Modeling.- 3. Classical Extreme Value Theory and Models.- 4. Threshold Models.- 5. Extremes of Dependent Sequences.- 6. Extremes of Non-Stationary Sequences.- 7. A Point Process Characterization of Extremes.- 8. Multivariate Extremes.- 9. Further Topics.- Appendix A: Computational Aspects.- Index.

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Quantifying dependence is a central theme in probabilistic and statistical methods for multivariate extreme values. Two situations are possible: one where, in a limiting sense, the extremes are dependent; the other where, in the same sense, the extremes are independent. This paper comprises an overview of the principal issues through a unified approach which encompasses both these situations. Novel diagnostic measures for dependence are also developed which provide complementary information about different aspects of extremal dependence. The paper is written in an elementary style, with the methodology illustrated by application to theoretical examples and typical data-sets. These data-sets and the S-plus functions used for the analyses are available online.

Dependence Measures for Extreme Value Analyses

A parametric model is developed and fitted to English league and cup football data from 1992 to 1995. The model is motivated by an aim to exploit potential inefficiencies in the association football betting market, and this is examined using bookmakers' odds from 1995 to 1996. The technique is based on a Poisson regression model but is complicated by the data structure and the dynamic nature of teams' performances. Maximum likelihood estimates are shown to be computationally obtainable, and the model is shown to have a positive return when used as the basis of a betting strategy.

Modelling Association Football Scores and Inefficiencies in the Football Betting Market

SUMMARY Understanding and quantifying the behaviour of a rainfall process at extreme levels has important applications for design in civil engineering. As in the extremal analysis of any environmental process, estimates often are required of the probability of events that are rarer than those already recorded. As data on extremes are scarce, all available sources of information should be used in inference. Consequently, research has focused on the development of techniques that make optimal use of available data. I n this paper a daily rainfall series is analysed within a Bayesian framework, illustrating how the careful elicitation of prior expert information can supplement data and lead to improved estimates of extremal behaviour. For example, using the prior knowledge of an expert hydrologist, a Bayesian 95% interval estimate of the 1 00-year return level for daily rainfall is found to be approximately half of the width of the corresponding likelihoodbased confidence interval,

A Bayesian Analysis of Extreme Rainfall Data

In recent research on extreme value statistics, there has been an extensive development of threshold methods, first in the univariate case and subsequently in the multivariate case as well. In this paper, an alternative methodology for extreme values of univariate time series is developed, by assuming that the time series is Markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions. A new likelihood representation for threshold methods is presented which we apply to a Markovian time series. An important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events. We address this issue by showing how a theory of compound Poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest. The methods are illustrated by application to temperature data.

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Stuart Coles

Papers

An Introduction to Statistical Modeling of Extreme Values

Dependence Measures for Extreme Value Analyses

Modelling Association Football Scores and Inefficiencies in the Football Betting Market

A Bayesian Analysis of Extreme Rainfall Data

Markov chain models for threshold exceedances