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A large number of commonly used parametric Archimedean copula (AC) familiesare restricted to a single parameter, connected to a concordance measure suchas Kendall's tau. This often leads to poor statistical fits, particularly inthe joint tails, and can sometimes even limit the ability to model concordanceor tail dependence mathematically. This work suggests outer power (OP)transformations of Archimedean generators to overcome these limitations. Thecopulas generated by OP-transformed generators can, for example, allow one tocapture both a given concordance measure and a tail dependence coefficientsimultaneously. For exchangeable OP-transformed ACs, a formula for computingtail dependence coefficients is obtained, as well as two feasible OP ACestimators are proposed and their properties studied by simulation. Forhierarchical extensions of OP-transformed ACs, a new construction principle,efficient sampling and parameter estimation are addressed. By simulation,convergence rate and standard errors of the proposed estimator are studied.Excellent tail fitting capabilities of OP-transformed hierarchical AC modelsare demonstrated in a risk management application. The results show that the OPtransformation is able to improve the statistical fit of exchangeable ACs,particularly of those that cannot capture upper tail dependence or strongconcordance, as well as the statistical fit of hierarchical ACs, especially interms of tail dependence and higher dimensions. Given how comparably simple itis to include OP transformations into existing exchangeable and hierarchical ACmodels, this transformation provides an attractive trade-off betweencomputational effort and statistical improvement.

Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation