Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk

Chapter ElevenDependence Models

In this chapter we build upon the notions of dependence modelling in OpRisk described in Chapter 10 by presenting a variety of parametric models that practitioners may consider for construction of LDA dependence frameworks. We discuss specifically many families of parametric copula that are of direct relevance to OpRisk practitioners - explaining the specification and features of the models, the estimation of the parameters in such models via Inference Functions for the Margins (IFM), and the sampling from such models in an LDA framework. The copula models include:

• Gaussian copula;
• Student-T copula; skew Student-T copula; grouped Student-T copula and generalised Student-T copula;
• Archimedean copulas: Frank, Clayton, Gumbel, Joe; Mixture Archimedean copula; Heirarchical Archimedean copulas; Nested Archimedean copulas; Outer and Inner power transformed Archimedean copula;
• Levy copula; Max-stable models and Self-Chaining copula;
• Common factor models and factor copulas.

We then conclude this chapter with several examples of LDA models with dependence incorporated, including between frequency and severity models as well as common factor formulations. These act as small illustrative case studies for practitioners to see a complete development of such models that can be utilized and extended for practical application.

11.1 Introduction to Parametric Dependence Modeling Through a Copula

The extensive interest in copula modeling can largely be attributed ...