A Comparative Analysis of Correlation Approaches in Finance

Abstract

EDGAR LOBACHEVSKIYis the senior quantitative analyst at AlphaMetrix LLC in Chicago, IL. edgar.lobachevskiy@gmail.com GUNTER MEISSNERis the director of the master of financial engineering (MFE) program at the University of Hawaii and the CEO of Derivatives Software in Honolulu, HI. meissner@hawaii.edu "… correlation, while being one of the most ubiquitous concepts in modern finance and insurance, is also one of the most misunderstood concepts."-Embrechts et al. [1999] This article analyzes the most widely applied correlation approaches in finance. The authors first discuss primarily bottom-up approaches, such as correlating Brownian motions, the binomial correlation approach, lattice models with dynamic copulas, conditionally independent models, and the contagion correlation approach. New insights on the Gaussian copula, partly blamed for the global financial crisis of 2007-2008, are given. They then discuss top-down approaches, such as Vasicek's 1987 large homogeneous portfolio, inducing correlation in Markov chain models, and Giesecke's 2009 top-down contagion model. They address the mathematical properties of the correlation approaches. A follow-up article will empirically test the correlation approaches by using default data of the U.S. banking sector before and during the 2007-2008 crisis.

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