In recent years special attention has been devoted to the problem of finding a copula, the diagonal section and opposite diagonal section of which are known. For given diagonal function and opposite diagonal functions, we provide necessary and sufficient conditions for the existence of a copula to have these functions as diagonal and opposite diagonal sections. We make use of techniques related...

To examine the asymmetry of financial data in detail, we have considered both the tail dependence with diverse copulas and Jung et al.’s [8] directional dependence by copula. From the empirical study in this paper, we have found that the tail dependence by Patton’s [11] modified symmetrized Joe-Clayton copula function did not show the asymmetry property sufficiently because there is no tail dep...

The valuation of basket default swaps depends crucially on the joint default probability of the underlying assets in the basket. It is known that this probability can be modeled by means of a copula function which links the marginal default probabilities to a joint probability. The valuation bears risk due to the uncertainty of the copula, the relation of the assets to each other and the margin...

We introduce a dimension reduction technique based on extreme observations. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a fairly general model for the copula. We assume an elliptical copula to describe the extreme dependence structure, which preserves a ’correlation-like’ structure in the extremes. Based on the tail ...

The class of multivariate Archimedean copulas is defined by using a realvalued function called the generator of the copula. This generator satisfies some properties, including d-monotonicity. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation ac...

In this paper, we consider different issues related to Archimedean copulae and positive dependence. In the first part, we characterize Archimedean copulae that possess positive dependence properties such as multivariate total positivity of order 2 ðMTP2Þ and conditionally increasingness in sequence. In the second part, we investigate conditions for exchangeable binary sequences to admit an Arch...

In this paper we suggest the adoption of copula functions in order to price bivariate contingent claims. Copulas enable us to imbed the marginal distributions extracted from vertical spreads in the options markets in a multivariate pricing kernel. We prove that such kernel is a copula function, and that its super-replication strategy is represented by the Fréchet bounds. As applications, we pro...

This short survey of copulas presents their properties, tries to stress their relevance for statistics and their connection with Markov processes and conditional expectations. 1 What is a copula? Copul were introduced by Sklar(1959). The reader is referred to Schweizer and Sklar (1983), Schweizer (1991), Sklar (1973), Sklar (1996), Nelsen (1999). A copula is a function C : [0; 1] ]0; 1[! ]0; 1[...

This paper presents an analysis of Irish clefting couched within LexicalFunctional Grammar. In Irish, cleft sentences are formed using two syntactic permutations. First, a copula is introduced, taking the clefted phrase or word as a predicate. Second, a relative clause is formed containing the remaining material of the original sentence. This basic pattern is valid across a variety of languages...

In this paper,we propose novelmethods of quantifying expert opinion about prior distributions formultinomial models. Two different multivariate priors are elicited using median andquartile assessments of themultinomial probabilities. First, we start by eliciting a univariate beta distribution for the probability of each category. Then we elicit the hyperparameters of the Dirichlet distribution,...