Beyond Correlations: The Use and Abuse of Copulas in Economic Capital Calculations

Abstract

Copulas have become a buzzword in recent years in the academic community, and practitioners are paying more and more attention to the choice of a copula in risk management applications.

This paper gives a non-technical and pedagogical introduction to the topic of copulas and explains their role for economic capital calculations.

Risk professionals may be tempted to dress up models by using sophisticated tools like for instance copulas. This is because these toys give them the possibility to give a scientific flavour and "serieux" to their models, and as such may serve as "an umbrella" towards the different stakeholders involved.

We provide examples to show that models that involve complicated copulas are by no means better than simple but robust and transparent models and do not always add value. However, building a simple as possible, but not too simple, model requires significant actuarial training and expertise.

Keywords: Copula, Economic Capital, Basel II, Solvency II, Correlations, Value-at-Risk