The paper presents an overview of financial applications of copulas. Copulas permit to represent joint distribution functions by splitting the marginal behavior, embedded in the marginal distributions, from the dependence, captured by the copula itself. The splitting proves to be very helpful not only in the modelling phase, but also in the estimation or simulation one. Essentially, it provides...

Any multivariate density can be decomposed through successive conditionings into basic building blocks involving only pairs of variables. The various ways in which this can be done are called regular vines; C-vines and D-vines are prime examples of such structures. A pair-copula construction (PCC) is a modelling strategy in which conditional and unconditional bivariate copula densities are assi...

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...

Multiplicative error models (MEM) became a standard tool for modeling conditional durations of intraday transactions, realized volatilities and trading volumes. The parametric estimation of the corresponding multivariate model, the so-called vector MEM (VMEM), requires a specification of the joint error term distribution, which is due to the lack of multivariate distribution functions on R+ def...

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 paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best-fit copula. Thereafter, simulation of copulas and bivariat...

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In thi...

A copula is a function which joins (or 'couples') a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

The question as to the role that correlated activity plays in the coding of information in the brain continues to be one of the most important in neuroscience. One approach to understanding this role is to formally model the ensemble responses as multivariate probability distributions. We have previously introduced alternatives to linear assumptions of multivariate Gaussian dependence for spike...