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...

Estimation of Distribution Algorithms (EDAs) are implemented mainly by the three steps: selecting the promising subset from the current population, modeling the distribution of the selected population and sampling from the estimated model. Modeling and sampling are key steps of EDAs. They are also research topic of copula theory to represent the multivariate joint distribution by a copula and t...

copula functions are powerful tools that describe dependence structure of multi- dimension random variables and are considered as one of the newest tools for risk management. one application of copula functions in risk management is calculating value at risk that can assert is the most widely used risk measures in financial institutions. in this article which primary goal is estimating more acc...

Gaussian copula is by far the most popular copula used in the financial industry in default dependency modeling. However, it has a major drawback — it does not exhibit tail dependence, a very important property for copula. The essence of tail dependence is the interdependence when extreme events occur, say, defaults of corporate bonds. In this paper we show that some tail dependence can be rest...

Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for th...

This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and ...

Empirical copula is a non-parametric algorithm to estimate the dependence structure of highdimensional arbitrarily distributed data. The computation of empirical copula is, however, very costly so that it cannot be implemented into applications at a real-time context. In this paper, fuzzy empirical copula is proposed to reduce the computation time of dependence structure estimation. First, a br...