Abstract
We explore several copula models of the joint distribution of national stock indices including FGM and Gaussian copulas and representatives of the Archimedean family. We compare the methods of estimation based on maximum likelihood including fully parametric and semi-parametric models built on empirical margins. Criteria for comparison of multiple bivariate copula models are suggested, based on empirical concordance, joint empirical distribution functions, and the patterns of the tail dependence. Five different copulas are analyzed and the model selection procedures are described. The conclusion suggesting that Frank copula appears to be the most appropriate model is compared with the results of other studies. Application of the models constructed is illustrated by calculation of the probabilities of catastrophic events (simultaneous stock index drop).