Factor copulas through a vine structure

Copula functions have been widely used in actuarial science, nance andeconometrics. Though multivariate copulas allow for a flexible specication of the dependence structure of economic variables, they are not particularly tempting in high dimensional contexts. A factor model which involves copula functions has already proved to be a powerful tool in credit risk applications.We exploit a recent approach to obtain a factor copula model based on a vine structure, which enables to model the dependence and conditional dependence of variables through a representation of a cascade of arbitrary bivariate copulas. The contribution of this paper consists into applying the vine copula model in order to derive a non linear three factor model. In particular, we draw the three factor model of Fama and French (1992). According to the Inference for Margins (IFM) method, we have computed, separately, the margins and the copula parameters via maximum likelihood estimation. Finally, tail dependence measures are given for the implied estimated copula.