Modeling Dependence in High Dimensions With Factor Copulas

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.

The Realized Hierarchical Archimedean Copula in Risk Modelling

“…However, elliptical copulae are not able to capture the stylized facts observed in financial data. The factor approach overcomes this limitation and has attracted attention in the copula literature over the last decade, see, for example, Andersen and Sidenius (2004), Van der Voort (2007), Krupskii and Joe (2013), Oh and Patton (2017). The limitation of the factor copula models is that the likelihood function is often not known in closed form, which complicates the estimation of the parameters.…”

The Core, Periphery, and Beyond: Stock Market Comovements among EU and Non‐EU Countries

“…Christoffersen, Errunza, Jacobs and Langlois (2012) and Lucas, Schwaab and Zhang (2014) use skewed t copula, which allows for the possibility of an asymmetric dependence. Other variations include the symmetrized Joe-Clayton(Patton, 2006) and the factor copula(Oh and Patton, 2017).9 Tail dependence coefficients measure the probability of two variables concurrently assuming extremely positive or negative values. One could argue that quantile dependence offers a more comprehensive approach to measuring dependence, as compared with tail dependence, as it explores all realizations of random variables.…”

Dependent defaults and losses with factor copula models

“…Such approaches alleviate the curse of dimensionality by considering a smaller set of latent variables, conditional upon which the random variables of interest are assumed independent. Arguably the main di erence between the methods presented in [45,46] and [35,36] is that copulas proposed in the former can only be simulated, whereas those in the latter admit closed form expressions. In fact, it can be shown the factor copulas from [35,36] are a special case of pair-copula constructions (PCCs).…”

“…Conversely, members of the Archimedean family have a small and xed number of parameters, independently of the dimension. Recently, high-dimensional copulas using a factor structure have been constructed independently by [45,46] and [35,36]. Such approaches alleviate the curse of dimensionality by considering a smaller set of latent variables, conditional upon which the random variables of interest are assumed independent.…”