The Archimedean copulas measure of the risk characteristic for the tail dependent asset returns

Copulas represent a useful approach to understanding and modeling dependent components of random variables that allows us to focus explicitly on the dependence structure. This paper aims to seek out the most appropriate copula which can model the dependence structure and measure the risk characteristic for the tail dependent asset returns. Based on the empirical data from the financial market, we begin with the analysis of the marginal choice for the copulas by comparing three different Archimedean copulas with respect to nonparametric kernel density estimation, semiparametric estimation and the estimation based on full empirical assumption of the margins, on the basis of which, we conduct the statistical estimation of the copula parameters using inference functions for margins (IFM) and canonical maximum likelihood (CML) methods. A procedure is thereafter proposed for identifying the most suitable copula. We then calibrate copula functions to recover the joint tail distribution and to quantify the magnitude of tail dependence by comparing different Archimedean copulas with the nonparametric empirical one. We present in detail from different aspects that Gumbel among three Archimedean members is the most suitable copula that has the desired property which is in accordance with the empirical behavior of our market data.