Financial Applications of Copula Functions - Thierry Roncalli

Financial Applications of Copula FunctionsJean-Fr ed eric Jouanin, Ga el Riboulet and Thierry RoncalliGroupe de Recherche Op erationnelle, Cr edit Lyonnais, FranceAbstractCopula Functions have been introduced recently in finance. They are a general tool to constructmultivariate distributions and to investigate dependence structure between random variables. In thispaper, we show that Copula Functions may be extensively used to solve many Financial problems. Asexamples we show how to them to monitor the market risk of basket products, to measure the credit riskof a large pool of loans and to compute capital requirements for operational Classification:G10 Key words: Copula , risk management, market risk, credit risk, operational risk1 IntroductionOne of the main issues in risk management is the aggregation of individual risks. This problem can beeasily solved or at least discarded by assuming that the random variables modelling individual risks areindependent or are only dependent by means of a common factor, so that we can reduce to the case ofindependent variables, by eventually adding one new variable (describing the common factor) to the set ofthe problem becomes much more involved when one wants to model fully dependent random variables or,when one does not know what the exact joint distribution is, to produce a large set of dependence betweenthe given individual risks.

Financial Applications of Copula Functions Jean-Fr´ed´eric Jouanin, Ga¨el Riboulet and Thierry Roncalli Groupe de Recherche Op´erationnelle, Cr´edit Lyonnais, France

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  Applications, Financial, Functions, Cupolas, Financial applications of copula functions

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