Factor Copulas through a vine structure

Copula functions have been widely used in actuarial science, finance and econometrics. Though multivariate copulas allow for a flexible specification of the dependence structure of economic variables, in high dimensional contexts they are not particularly attractive. A factor model which involves the copula functions has proved to be a powerful tool in credit risk applications, e.g. for the pricing of CDO, due to its capability in describing, in a both flexible and tractable way, the joint default for a large number of names within a semi-analytical framework. Many of the factor copula models proposed in theoretical and empirical application are embedded into a stochastic correlations framework or in analysing simulation and pricing, not considering the estimation of copula parameters. We exploit a new approach to obtain a factor copula model based on a vine structure for the asset returns, which enables to modeling the dependence and conditional dependence of variables through a representation of a cascade of arbitrary bivariate copulas. According to the Inference for Margins (IFM) method, we have computed, separately, the margins and the copula parameters via maximum likelihood estimation. In the first, GARCH models for margins are applied and then, given the conditional independence of the transformed standardized residuals with respect to common factors, vine copulas are estimated, providing the parameters of an “implied copula” for the asset returns. Finally, a tail dependence measure is given for the implied copula estimated.