Michel Dacorogna, Tail-Dependence an Essential Factor for

Number of Observations mattersless than Dependence ModelsWe see that the elliptical copulas keep a systematic biaswhatever the number of observationsThe Archimedean copulas fit much better the theoretical valuewith Clayton doing it the best, as expectedThe error of the estimation decreases with the number ofobservations and remains at a certain level even with 50’000observationsThe structure of the dependence (hierarchical or flat) does notaffect really the diversification benefit with hierarchical beingslightly better for Archimedean copulasWhen the dependence is asymmetric (as it is usually the casefor insurance liabilities), it is difficult to model it with symmetricdependence models (use asymmetric copulas)Tail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 201231Agenda1 Risk-Adjusted Capital and dependence2 Description of the model3 Influence of the number of observations on calibration4 Influence of dependence structure and models5 Ways to model the dependence6 ConclusionTail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 201232