In this paper, we propose a method how to construct density weighting functions from Copulas. The notion of Copula was introduced by A. Sklar in 1959. A Copula is a dependence function to construct a bivariate distribution function that links joint distributions to their marginals. Other forms of dependence function, based on density weighing functions, have also been developed. The proposed me...

In this paper, we briefly review the basics of copula theory and the problem of estimating Value at Risk (VaR) of portfolio composed by several assets. We present two VaR estimation models in which each return series is assumed to follow AR(1)-GARCH(1, 1) model and the innovations are simultaneously generated using Gaussian copula and Student t copula. The presented models are applied to estima...

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of a...

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information abo...

modeling dependence structure in financial economics is of paramount importance when estimating portfolio’s value at risk, since risk of an asset in addition to its own behavior is also dependent on the behavior of other assets in the portfolio. application of joint distribution copula is one of the methods for incorporation dependence at lower and upper tail of returns’ distribution in financi...

Abstract. This study introduces a new approach to problem of estimating parameter(s) of a given copula. More precisely, using the concept of the generalized linear models (GLM) accompanied with least square method, we introduce an estimation method, say GLM-method. A simulation study has been conducted to provide a omparison among the inversion of Kendal’s tau, the inversion of Spearman’s rho,...

In order to study copula families that have different tail patterns and tail asymmetry than multivariate Gaussian and t copulas, we introduce the concepts of tail order and tail order functions. These provide an integrated way to study both tail dependence and intermediate tail dependence. Some fundamental properties of tail order and tail order functions are obtained. For the multivariate Arch...

In spite of its simplicity, the popular One Factor Gaussian Copula model remains the market standard for the valuation of CDO tranches and n-th to default. It suffers however from well-know weaknesses, mainly due to the tail behavior of the Normal distribution (namely : the tails are too light, and there is no tail dependence, whatever is the copula correlation). Alternative models have been pr...

Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although...

In this paper, we propose a score fusion method using a mixture copula that can consider complex dependencies between multiple relevance scores in order to improve the effectiveness of information retrieval. The combination of multiple relevance scores has been shown to be effective in comparison with a single score. Widely used score fusion methods are linear combination and learning to rank. ...