Conditional normal extreme-value copulas

Measure of financial risk using conditional extreme value copulas with EVT margins

In this paper we propose a method to estimate the value-at-risk (VaR) of a portfolio based on a combination of time series, extreme value theory and copula fitting. Given multivariate financial data, we use a univariate ARMA-GARCH model for each return series. We then fit a generalized Pareto distribution to the tails of the residuals to model the distributions of marginal residuals, followed b...

Modelling the Dependence of Parametric Bivariate Extreme Value Copulas

In this study, we consider the situation where contraints are made on the domains of two random variables whose joint copula is an extreme value model. We introduce a new measure which characterize these conditional dependence. We proved that every bivariate extreme value copulas is totally characterized by a conditional dependence function. Every twodimensional distribution is also shown to be...

Rank - Based Inference for Bivariate Extreme - Value Copulas

Consider a continuous random pair (X, Y) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. In this paper, rank-based versions of these esti-mators are proposed for the more commo...

Multivariate Fréchet copulas and conditional value-at-risk

Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most desirable properties that a multivariate statistical model should satisfy. In particular, the bivariat...

Extreme distribution functions of copulas