Modelling Dependence in High Dimensions with Factor Copulas
FEDS Working Paper No. 2015-0511
http://dx.doi.org/10.17016/FEDS.2015.0511
42 Pages Posted: 26 Jul 2015
Date Written: May 18, 2015
Abstract
This paper presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for relatively high dimensional applications, involving fifty or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied tail dependence using extreme value theory, and we verify that simulation-based estimation using rank statistics is reliable even in high dimensions. We consider "scree" plots to aid the choice of the number of factors in the model. The model is applied to daily returns on all 100 constituents of the S&P 100 index, and we find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. We also show that factor copula models provide superior estimates of some measures of systemic risk.
Keywords: copulas, correlation, dependence, systemic risk, tail dependence
JEL Classification: C31, C32, C51
Suggested Citation: Suggested Citation