Efficient sampling algorithms for both Archimedean and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a...

The package nacopula provides procedures for constructing nested Archimedean copulas in any dimensions and with any kind of nesting structure, generating vectors of random variates from the constructed objects, computing function values and probabilities of falling into hypercubes, as well as...

Companies in the same industry sector are usually more correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. Despite the many stock return models taking this fact into account, there are only a few credit...

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss...

Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference it is...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

A new class of copulas referred to as “Sibuya copulas” is introduced and its properties are investigated. Members of this class are of a functional form which was first investigated in the work of M. Sibuya. The construction of Sibuya copulas is based on an increasing stochastic process...

Necessary and sufficient conditions for the subadditivity of Value-at-Risk (V aRα) for portfolios of bonds are presented under various dependence assumptions. For sufficiently large α, V aRα is subadditive. However, for any α one can construct portfolios for which V aRα is superadditive.

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...