Multiple risk factor dependence structures: Copulas and related properties

Abstract

Abstract. Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the 'right' copula is not an easy task, and the temptation to prefer a tractable rather than a meaningful candidate from the encompassing copulas toolbox is strong. The ubiquitous applications of the Gaussian copula is just one illuminating example.Speaking generally, a 'good' copula should conform to the problem at hand, allow for asymmetry in the domain of definition and exhibit some extent of tail dependence. In this paper we introduce and study a new class of Multiple Risk Factor (MRF) copula functions, which we show are exactly such. Namely, the MRF copulas (1) arise from a number of meaningful default risk specifications with stochastic default barriers, (2) are in general non-exchangeable and (3) possess a variety of tail dependences. That being said, the MRF copulas turn out to be surprisingly tractable analytically.

Hypothesis testing for tail dependence parameters on the boundary of the parameter space

“…In Cui and Zhang (2018) and Zhao and Zhang (2018), max-linear models are used to model a latent factor structure for financial returns. Finally, the Marshall-Olkin model (Embrechts et al, 2003;Segers, 2012) is a submodel that is frequently used in practice, see for instance Burtschell et al (2009), Su and Furman (2017) or Brigo et al (2018).…”