1999], Correlation and dependency in risk management : properties and pitfalls

Abstract. Modern risk management calls for an understanding of stochastic de-pendence going beyond simple linear correlation. This paper deals with the static (non-time-dependent) case and emphasizes the copula representation of depen-dence for a random vector. Linear correlation is a natural dependence measure for multivariate normally and, more generally, elliptically distributed risks but other dependence concepts like comonotonicity and rank correlation should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of nding multivariate models which are consistent with prespecied marginal dis-tributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed. 1