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Beyond Correlation: Extreme Comovements Between Financial Assets
, 2002
"... This paper inv estigates the potential for extreme comov ements between financial assets by directly testing the underlying dependence structure. In particular, a tdependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three ..."
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Cited by 34 (5 self)
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This paper inv estigates the potential for extreme comov ements between financial assets by directly testing the underlying dependence structure. In particular, a tdependence structure, deriv ed from the Student t distribution, is used as a proxy to test for this extremal behav#a(0 Tests in three di#erent markets (equities, currencies, and commodities) indicate that extreme comov ements are statistically significant. Moreov er, the "correlationbased" Gaussian dependence structure, underlying the multiv ariate Normal distribution, is rejected with negligible error probability when tested against the tdependencealternativ e. The economic significance of these results is illustratedv ia three examples: comov ements across the G5 equity markets; portfoliov alueatrisk calculations; and, pricing creditderiv ativ es. JEL Classification: C12, C15, C52, G11. Keywords: asset returns, extreme comov ements, copulas, dependence modeling, hypothesis testing, pseudolikelihood, portfolio models, risk management. # The authorsw ould like to thankAndrew Ang, Mark Broadie, Loran Chollete, and Paul Glasserman for their helpful comments on an earlier version of this manuscript. Both authors arewS; the Columbia Graduate School of Business, email: {rm586,assaf.zeevi}@columbia.edu, current version available at www.columbia.edu\# rm586 1 Introducti7 Specification and identification of dependencies between financial assets is a key ingredient in almost all financial applications: portfolio management, risk assessment, pricing, and hedging, to name but a few. The seminal work of Markowitz (1959) and the early introduction of the Gaussian modeling paradigm, in particular dynamic Brownianbased models, hav e both contributed greatly to making the concept of co rrelatio almost synony...
VaR and Expected Shortfall in Portfolios of Dependent Credit Risks: Conceptual and Practical Insights
 JOURNAL OF BANKING AND FINANCE
, 2002
"... In the first part of this paper we address the noncoherence of valueatrisk (VaR) as a risk measure in the context of portfolio credit risk, and highlight some problems which follow from this theoretical deficiency. In particular, a realistic demonstration of the nonsubadditivity of VaR is giv ..."
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Cited by 29 (1 self)
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In the first part of this paper we address the noncoherence of valueatrisk (VaR) as a risk measure in the context of portfolio credit risk, and highlight some problems which follow from this theoretical deficiency. In particular, a realistic demonstration of the nonsubadditivity of VaR is given and the possibly nonsensical consequences of VaRbased portfolio optimisation are shown. The second part of the paper discusses VaR and expected shortfall estimation for large balanced credit portfolios. All standard industry models (Creditmetrics, KMV, CreditRisk+) are presented as Bernoulli mixture models to facilitate their direct comparison. For homogeneuous groups it is shown that measures of tail risk for the loss distribution may be approximated in large portfolios by analysing the tail of the mixture distribution in the Bernoulli representation. An example is given showing that, for portfolios of lower quality, choice of model has some impact on measures of extreme risk.
Copulas and Credit Models
 RISK October
, 2001
"... this article we focus on the latent variable approach to modelling credit portfolio losses. This methodology underlies all models that descend from Merton's firmvalue model (Merton 1974). In particular, it underlies the most important industry models, such as the model proposed by the KMV corporati ..."
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Cited by 21 (2 self)
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this article we focus on the latent variable approach to modelling credit portfolio losses. This methodology underlies all models that descend from Merton's firmvalue model (Merton 1974). In particular, it underlies the most important industry models, such as the model proposed by the KMV corporation and CreditMetrics. In these models default of an obligor occurs if a latent variable, often interpreted as the value of the obligor's assets, falls below some threshold, often interpreted as the value of the obligor's liabilities. Dependence between default events is caused by dependence between the latent variables. The correlation matrix of the latent variables is often calibrated by developing factor models that relate changes in asset value to changes in a small number of economic factors. For further reading see papers by Koyluoglu and Hickman (1998), Gordy (2000) and Crouhy, Galai, and Mark (2000). A core assumption of the KMV and CreditMetrics models is the multivariate normality of the latent variables. However there is no compelling reason for choosing a multivariate normal (Gaussian) distribution for asset values. The aim of this article is to show that the aggregate portfolio loss distribution is often very sensitive to the exact nature of the multivariate distribution of the latent variables. This is not simply a question of asset correlation. Even when individual default probabilities of obligors and the matrix of latent variable correlations are held fixed, it is still possible to develop alternative models which lead to much heaviertailed loss distributions. A useful source of alternative models is the family of multivariate normal mixture distributions, which includes Student's t distribution and the generalized hyperbolic distribution. In most cases it is...
Credit risk modeling and valuation: an introduction
 In D. Shimko. Credit Risk: Models and Management
, 2004
"... ..."
Pricing multiname credit derivatives: heavy tailed hybrid approach
, 2002
"... In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are in ..."
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Cited by 13 (1 self)
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In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are instruments with payoffs that are contingent on the default realization in a portfolio of names. The modeling of dependent defaults is difficult because there is very little historical data available about joint defaults and because the prices of those instruments are not quoted. Therefore, the models cannot be calibrated, neither to defaults nor to prices. In this paper, we present a methodology for the estimation, simulation, and pricing of multiname contingent instruments. Our model is a hybrid of the wellknown structural and reduced form approaches for modeling defaults. The dependence structure of our model is of a tcopula that possesses nontrivial tail dependence. The tcopula allows for more joint extreme events, which have a big impact on the prices of multiname instruments, e.g. n thtodefault baskets and CDOs. We demonstrate this impact with n thtodefault baskets.
Tail behavior of credit loss distributions for general latent factor models. Paper presented at
 the Third Joint Central Bank Research Conference on Risk Measurement and Systemic Risk (www.bis.org/cgfs/cgfsconf2002prog.htm
, 2002
"... Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the comovements in defaults over time, we assume that defaults are triggered by a general, possibly nonlinear, factor model involving both systematic and idiosyncra ..."
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Cited by 7 (1 self)
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Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the comovements in defaults over time, we assume that defaults are triggered by a general, possibly nonlinear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk +. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model’s functional form and the tail properties of the model’s risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk + approach to modeling portfolio credit risk. Key words: portfolio credit risk; extreme value theory; tail events; tail index; factor models; economic capital; portfolio quality; secondorder expansions.
Extremes in Economics and the Economics of Extremes
 In: Extreme Values in Finance, Telecommunications, and the Environment
, 2001
"... This paper is based on a talk with the above title given at the SemStat meeting on Extreme Value Theory and Applications in Gothenburg on December 13, 2001 ..."
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Cited by 6 (4 self)
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This paper is based on a talk with the above title given at the SemStat meeting on Extreme Value Theory and Applications in Gothenburg on December 13, 2001
Credit Risk Models II: Structural Models
 FINANCIAL MATHEMATICS, KING’S COLLEGE
, 2003
"... This report reviews the structural approach for credit risk modelling, both considering the case of a single firm and the case with default dependences between firms. In the single firm case, we review the Merton (1974) model and first passage models, examining their main characteristics and extensi ..."
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Cited by 5 (3 self)
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This report reviews the structural approach for credit risk modelling, both considering the case of a single firm and the case with default dependences between firms. In the single firm case, we review the Merton (1974) model and first passage models, examining their main characteristics and extensions. Liquidation process models extend first passage models to account for the possibility of a lengthy liquidation process which might or might not end up in default. Finally, we review structural models with state dependent cash flows (recession vs. expansion) or debt coupons (ratingbased). The estimation of structural models is addressed, covering the different ways proposed in the literature. In the second part of the text, we present some approaches to model default dependences between firms. They account for two types of default correlations: cyclical default correlation and contagion effects. We close the paper with a brief mention of factor models.