In this paper we introduce two methods for the construction of asymmetric multivariate copulas. The …rst is connected with products of copulas. The second approach generalises the Archimedean copulas. The resulting copulas are asymmetric and may have more than two parameters in contrast to most of the parametric families of copulas described in the literature. We study the properties of the pro...

This paper develops a method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. As the association between the underlying assets may vary over time, the dynamic copula with time-varying parameter offers a better alternative to any static model for dependence structure and even to the dynamic copula model determined by dynamic depe...

Besides their advantage in modelling tail-dependency, the main drawback of standard non-Gaussian copula is the homogeneity in the tail dependency parameter. Several approaches to solve this are meanwhile developed, hierachical copula, the grouped t-copula and the heterogeneous t-copula as recently described by Luo and Shevchenko [1]. We will show results from a concrete implementation of a fact...

This paper concerns the application of copula functions in VaR valuation. The copula function is used to model the dependence structure of multivariate assets. After the introduction of the traditional Monte Carlo simulation method and the pure copula method we present a new algorithm based on mixture copula functions and the dependence measure, Spearman’s rho. This new method is used to simula...

The paper considers likelihood-based estimation of multivariate models, in which only marginal distributions are correctly specified. The unknown joint distribution is modelled with a copula function, which may be misspecified. In a GMM framework, we study robustness and efficiency of resulting estimators, propose improvements to existing estimators and discuss tests of copula validity. It is s...

Based on the trivariate pair-copula construction for the bivariate linear circular copula by Perlman and Wellner (Symmetry 3:574-99, 2011) and the Theorem of Carathéodory, which states that any valid correlation matrix is a finite convex combination of extreme correlation matrices, we generate a class of closed-form analytical 3-universal copulas. We derive explicit product and lifting copula f...

Abstract. We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section for the existence of the optimal copula and give a closed formula for its entropy. We also ...

This chapter introduces copula functions and the use of the Gaussian copula function to model probabilistic dependencies in supervised classification tasks. A copula is a distribution function with the implicit capacity to model non linear dependencies via concordance measures, such as Kendall’s τ . Hence, this chapter studies the performance of a simple probabilistic classifier based on the Ga...

A hierarchical family of integrals based on a fixed copula is introduced and discussed. The extremal members of this family correspond to the inner and outer extension of integrals of basic functions, the copula under consideration being the corresponding multiplication. The limits of the members of the family are just copulabased universal integrals as recently introduced in Klement et al. (IE...

Abstract The Pearson product-moment correlation commonly used as statistical dependence measure was developed assuming normal marginal and addresses only linear dependence. In most applications, the distribution is assumed to be a multivariate normal or lognormal for tractable calculus even if the assumption may not be appropriate. A copula based approach couples marginal distributions to form ...