Multiple risk factor dependence structures: Distributional properties

TL;DR

This paper introduces the Multiple Risk Factor (MRF) dependence structures, extending CreditRisk+ to model portfolios with multiple risk factors and heavy-tailed distributions, applicable to credit and insurance risk modeling.

Contribution

The paper develops a new class of dependence structures that generalize existing models, capturing complex dependencies and heavy tails in risk portfolios.

Findings

Extends CreditRisk+ to multiple risk factors

Provides a family of multivariate distributions with Pareto margins

Applicable to modeling dependent heavy-tailed insurance risks

Abstract

We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with conditionally exponential and dependent hitting (or occurrence) times. On the other hand, the MRF structures can be seen as an encompassing family of multivariate probability distributions with univariate margins distributed Pareto of the 2nd kind, and in this role they can be used to model insurance risk portfolios of dependent and heavy tailed risk components.