The knowledge of the multivariate stochastic dependence between the returns of asset classes is of importance for many finance applications, such as, e.g., asset allocation or risk management. By means of goodness-of-fit tests, it is analyzed for a multitude of portfolios consisting of different asset classes whether the stochastic dependence between the portfolios’ constituents can be adequate...

Copulas are statistical tools for modelling the multivariate structure between variables in a distribution free way. They are beginning to be used in financial literature as an alternative to the multivariate normal. After reviewing the main properties of bivariate and multivariate copulas, three multivariate families are presented: the classical multivariate normal, the Fairlie-Gumbel-Morganst...

The measure for expert dependence proposed by Jouini and Clemen (clemen) is implemented for expert judgement data gathered at the T.U. Delft. Experts show less dependence than might have been supposed, though more sensitive measures might reveal more. Clemen’s copula for aggregation is implemented and performance is compared with performance-based combinations for two illustrative cases.

Sklar’s theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of pboxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar’s theorem...

Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical 2-point copula for the evolved dark matter density fiel...

We discuss the general optimization problem of choosing a copula with minimum entropy relative to a specified copula and a computationally intensive procedure to solve its dual. These techniques are applied to constructing an empirical copula for CDO tranche pricing. The empirical copula is chosen to be as close as possible to the industry standard Gaussian copula while ensuring a close fit to ...

In this paper we use dynamic copulas method to price a CDO. We apply GOF test and binary segmentation procedure to detect the change of copula function. According to the result of the change point, we divide the time series into nine stages. In each stage, we use the best copula function to describe the default correlation. Our empirical results show that in different time period, the best copu...