Correlation and Dependence in Risk Management: Properties and Pitfalls

作者：Paul Embrechts, Alexander J. McNeil, Daniel Straumann · 发表于：Risk Management · 年份：2002 · DOI：10.1017/cbo9780511615337.008 · 被引用次数：2020 · 研究领域：Financial Risk and Volatility Modeling、Statistical Methods and Inference、Risk and Portfolio Optimization

Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This article deals with the static (nontime- 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. Introduction Correlation in finance and insurance In financial theory the notion of correlation is central. The Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) (Campbell, Lo & MacKinlay 1997) use correlation as a measure of dependence between different financial instruments and employ an elegant theory, which is essentially founded on an assumption of multivariate normally distributed returns, in order to arrive at an optimal portfolio selection. Although insurance ha...