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Copulas: A personal view
"... Copula modeling has taken the world of finance and insurance, and well beyond, by storm. Why is this? In this paper I review the early start of this development, discuss some important current research, mainly from an applications point of view, and comment on potential future developments. An alter ..."
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Cited by 38 (9 self)
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Copula modeling has taken the world of finance and insurance, and well beyond, by storm. Why is this? In this paper I review the early start of this development, discuss some important current research, mainly from an applications point of view, and comment on potential future developments. An alternative title of the paper would be “Demystifying the copula craze”. The paper also contains what I would like to call the copula mustreads. Keywords: copula, extreme value theory, Fréchet–Hoeffding bounds, quantitative risk management, Value–at–Risk 1
Multivariate extremes and the aggregation of dependent risks: Examples and counterexamples
 Extremes, 2008. ISSN 13861999 (Print) 1572915X (Online). URL http://www.springerlink.com/content/ 102890/?Content+Status=Accepted
"... Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counterexamp ..."
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Cited by 28 (7 self)
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Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss sub and superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counterexamples highlight the applicability of the main results obtained.
Conditioning on an extreme component: Model consistency and regular variation on cones
"... Abstract. Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector necessitating that each component satisfy a marginal domain of attraction condition. Heffernan and Tawn (2004) and Heffernan and Resnick (2007) developed an appro ..."
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Cited by 20 (7 self)
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Abstract. Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector necessitating that each component satisfy a marginal domain of attraction condition. Heffernan and Tawn (2004) and Heffernan and Resnick (2007) developed an approximation to the joint distribution of the random vector by conditioning that one of the components be extreme. The prior papers left unresolved the consistency of different models obtained by conditioning on different components being extreme and we provide understanding of this issue. We also clarify the relationship between the conditional distributions and multivariate extreme value theory. We discuss conditions under which the two models are the same and when one can extend the conditional model to the extreme value model. We also discuss the relationship between the conditional extreme value model and standard regular variation on cones of the form [0, ∞] × (0, ∞] or (0, ∞] × [0, ∞]. 1.
Pricing kthtodefault swaps under default contagion: the matrixanalytic approach
, 2006
"... We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is transla ..."
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Cited by 14 (3 self)
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We study a model for default contagion in intensitybased credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is translated into a Markov jump process which represents the default status in the credit portfolio. This makes it possible to use matrixanalytic methods to derive computationally tractable closedform expressions for singlename credit default swap spreads and k thtodefault swap spreads. We ”semicalibrate” the model for portfolios (of up to 15 obligors) against market CDS spreads and compute the corresponding k thtodefault spreads. In a numerical study based on a synthetic portfolio of 15 telecom bonds we study a number of questions: how spreads depend on the amount of default interaction; how the values of the underlying market CDSprices used for calibration influence k ththto default spreads; how a portfolio with inhomogeneous recovery rates compares with a portfolio which satisfies the standard assumption of identical recovery rates; and, finally, how well k ththto default spreads in a nonsymmetric portfolio can be approximated by spreads in a symmetric portfolio.
The Pareto copula, aggregation of risks and the emperor’s socks
 J. APPL. PROBAB., {WWW.MA.TUM.DE/STAT
, 2007
"... The copula of a multivariate distribution is the distribution transformed so that one dimensional marginal distributions are uniform. We review a different transformation of a multivariate distribution which yields standard Pareto for the marginal distributions and the resulting distribution we call ..."
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Cited by 13 (3 self)
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The copula of a multivariate distribution is the distribution transformed so that one dimensional marginal distributions are uniform. We review a different transformation of a multivariate distribution which yields standard Pareto for the marginal distributions and the resulting distribution we call the Pareto copula. Use of the Pareto copula has a certain claim to naturalness when considering asymptotic limit distributions for sums, maxima and empirical processes. We discuss implications for aggregation of risk and offer some examples.
Copula theory: an introduction
 In Copula Theory and Its Applications, Volume 198 of Lecture Notes in Statistics
, 2010
"... Abstract In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have been applied ..."
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Cited by 9 (0 self)
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Abstract In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have been applied
Bounds for the sum of dependent risks having overlapping marginals
, 2009
"... We describe several analytical and numerical procedures to obtain bounds on the distribution function of a sum of n dependent risks having fixed overlapping marginals. As an application, we produce bounds on quantilebased risk measures for portfolios of financial/actuarial interest. ..."
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Cited by 7 (2 self)
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We describe several analytical and numerical procedures to obtain bounds on the distribution function of a sum of n dependent risks having fixed overlapping marginals. As an application, we produce bounds on quantilebased risk measures for portfolios of financial/actuarial interest.
A survey of spatial extremes: Measuring spatial dependence and modeling spatial effects
 Revstat
, 2012
"... We survey the current practice of analyzing spatial extreme data, which lies at the intersection of extreme value theory and geostatistics. Characterizations of multivariate maxstable distributions typically assume specific univariate marginal distributions, and their statistical applications gener ..."
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Cited by 6 (1 self)
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We survey the current practice of analyzing spatial extreme data, which lies at the intersection of extreme value theory and geostatistics. Characterizations of multivariate maxstable distributions typically assume specific univariate marginal distributions, and their statistical applications generally require capturing the tail behavior of the margins and describing the tail dependence among the components. We review current methodology for spatial extremes analysis, discuss the extension of the finitedimensional extremes framework to spatial processes, review spatial dependence metrics for extremes, survey current modeling practice for the task of modeling marginal distributions, and then examine maxstable process models and copula approaches for modeling residual spatial dependence after accounting for marginal effects. KeyWords: copula; extremal coefficient; hierarchical model; madogram; maxstable process; multivariate extreme value distribution. AMS Subject Classification: • 62M30, 62H11, 62H20. 136 D. Cooley et al.A Survey of Spatial Extremes 137
Modelling Bonds and Credit Default Swaps Using a Structural Model with Contagion
 Affine Point Processes and Portfolio Credit Risk. Siam J
"... This paper develops a twodimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for ..."
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Cited by 5 (1 self)
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This paper develops a twodimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longerterm correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters. 1