Copulas in Finance

Abstract

The copula function describes a way of separating the marginal behaviour of individual risks and their dependence structure from a multivariate random vari- able. The approach of copulas is particularly useful when amultivariate distribution function has absolutely continuous marginal distribution functions, and the trans- formations are then invariant, hence copulas are invariant under strictly increasing transformations of the margins. The Kendall’s tau and Spearman’s rho defined in-terms of concordance as measures of association or dependence including tail dependence are also scale-invariant. Linear correlation is widely used to model dependence but has limitations as a measure of association and thus we opt to use copulas to analyze the dependence structure and build models for our different problems arising in risk management. We take a look at different copula families and highlight for some when they are most appropriate to use for a particular application and some of their drawbacks as diverse scenarios occur in different risk management models and the model should be able to reflect or capture the appropriate dependence structure.