Multiple risk factor dependence structures: Copulas and related properties

TL;DR

This paper introduces a new class of copulas called Multiple Risk Factor (MRF) copulas, which are designed to better model dependence structures in risk management by capturing asymmetry and tail dependence while remaining analytically tractable.

Contribution

The paper proposes and analyzes MRF copulas, a novel class that incorporates realistic default risk features and tail dependence, addressing limitations of traditional copulas.

Findings

MRF copulas are non-exchangeable and flexible in modeling tail dependence.

They are analytically tractable despite their complexity.

MRF copulas better fit real-world risk dependence scenarios.

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 specification 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.