Selection of copula model for inter-market dependence

Article type: Research Article

Authors: Gordeev, Vadim A.^a | Knyazev, Alexander G.^b | Shemyakin, Arkady E.^{c; *}

Affiliations: [a] Faculty of Economics, Moscow State University, Moscow, Russia | [b] Astrakhan State University, Astrakhan, Russia | [c] University of St. Thomas, St. Paul, MN, USA

Correspondence: [*] Corresponding author: Arkady E. Shemyakin, University of St. Thomas, 2115 Summit Ave, OSS 201, St. Paul, MN 55105, USA. E-mail: [email protected].

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).

Keywords: Stock index, inter-market risks, copula models, Gaussian copula, Archimedean copulas, Kendall's concordance, model selection

DOI: 10.3233/MAS-2012-0243

Journal: Model Assisted Statistics and Applications, vol. 7, no. 4, pp. 315-325, 2012