Empirical studies show that there is stronger dependency between large losses than large profit in financial market, which undermine the performance of using symmetric distribution for modeling these asymmetric. That is why the assuming normal joint distribution of returns is not suitable because of considering the linier dependence, and can be lead to inappropriate estimate of VaR. Copula theo...

This chapter introduces copula functions and the use of the Gaussian copula function to model probabilistic dependencies in supervised classification tasks. A copula is a distribution function with the implicit capacity to model non linear dependencies via concordance measures, such as Kendall’s τ . Hence, this chapter studies the performance of a simple probabilistic classifier based on the Ga...

Abstract The Pearson product-moment correlation commonly used as statistical dependence measure was developed assuming normal marginal and addresses only linear dependence. In most applications, the distribution is assumed to be a multivariate normal or lognormal for tractable calculus even if the assumption may not be appropriate. A copula based approach couples marginal distributions to form ...

By a theorem due to Sklar, a multivariate distribution can be represented in terms of its underlying margins by binding them together using a copula function. By exploiting this representation, the “copula approach” to statistical modelling proceeds by specifying distributions for each margin and a copula function. In this paper, a number of families of copula functions are given, with attentio...

This paper exposes the research being done about the incorporation of copula functions in supervised classification. It is shown, by means of pixel classification, the advantages that modeling dependencies provides to supervised classification and the benefits of doing it through copula functions which are not limited to linear dependencies. The experiments executed so far, show positive result...

We study the relations between tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses copula to model the dependence structure of a random vector, then upper exponent and tail order functions can...

This paper develops a novel approach to modeling and forecasting realized volatility (RV) measures based on copula functions. Copula-based time series models can capture relevant characteristics of volatility such as nonlinear dynamics and long-memory type behavior in a flexible yet parsimonious way. In an empirical application to daily volatility for S&P500 index futures, we find that the copu...

The paper deals with modeling of mutual dependencies among financial assets. Its aim is to investigate the impact of different copula assumptions on optimal portfolios, when CVaR optimization is used. Strategic asset allocation perspective is supposed. It is demonstrated that copula functions enable us to separate the modeling of dependency features of financial assets from the modeling of marg...

For a multivariate vector X with discrete components, we construct, by means of explicit randomised transformations of X, multivariate couplings of copula representers U associated to X. As a result, we show that any copula can be constructed in this manner, giving a full probabilistic characterisation of the set of copula functions associated to X. The dependence properties of these copula rep...