This paper proposes a new class of copula-based dynamic models for high dimension conditional distributions, facilitating the estimation of a wide variety of measures of systemic risk. Our proposed models draw on successful ideas from the literature on modeling high dimension covariance matrices and on recent work on models for general time-varying distributions. Our use of copula-based models enable the estimation of the joint model in stages, greatly reducing the computational burden. We use the proposed new models to study a collection of daily credit default swap (CDS) spreads on 100 U.S. …rms over the period 2006 to 2012. We …nd that while the probability of distress for individual …rms has greatly reduced since the …nancial crisis of 2008-09, the joint probability of distress (a measure of systemic risk) is substantially higher now than in the pre-crisis period.

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.

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