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Correlation and Dependence in Risk Management: Properties and Pitfalls

by Paul Embrechts of ETH-Zentrum,
Alexander McNeil of ETH-Zentrum, and
Daniel Straumann of ETH-Zentrum

August 9, 1999

Abstract: Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This paper deals with the static (non-time-dependent) case and emphasizes the copula representation of dependence 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 finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed.

Keywords: Risk management, correlation, elliptic distributions, rank correlation, dependence, copula, comonotonicity, simulation, Value-at-Risk, coherent risk measures.

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