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On an asymmetric extension of multivariate Archimedean copulas based on quadratic form

100%

Di Bernardino E., Rullière D.

Dependence Modeling

2016

tom 4

nr 1

An important topic in Quantitative Risk Management concerns the modeling of dependence among risk sources and in this regard Archimedean copulas appear to be very useful. However, they exhibit symmetry, which is not always consistent with patterns observed in real world data. We investigate extensions of the Archimedean copula family that make it possible to deal with asymmetry. Our extension is based on the observation that when applied to the copula the inverse function of the generator of an Archimedean copula can be expressed as a linear form of generator inverses. We propose to add a distortion term to this linear part, which leads to asymmetric copulas. Parameters of this new class of copulas are grouped within a matrix, thus facilitating some usual applications as level curve determination or estimation. Some choices such as sub-model stability help associating each parameter to one bivariate projection of the copula. We also give some admissibility conditions for the considered copulas. We propose different examples as some natural multivariate extensions of Farlie-Gumbel-Morgenstern or Gumbel-Barnett.

On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators

100%

Di Bernardino E., Rullière D.

Dependence Modeling

2013

tom 1

1-36

We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these expressions are proposed and their convergence is investigated. We provide confidence bands for the estimated generators. Numerical illustrations show the empirical performance of these estimators.

Ograniczanie wyników

2 Dependence Modeling

2 Di Bernardino E.

2 Rullière D.

1 2016

1 2013

Wyniki wyszukiwania

On an asymmetric extension of multivariate Archimedean copulas based on quadratic form

On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators