A Comparative Analysis of Correlation Approaches in Finance

This paper analyses the most widely applied correlation approaches in finance. We first discuss primarily bottom-up approaches, as correlating Brownian motions (Heston 1993), the binomial correlation approach (Lucas 1995), Copulas (Sklar 1959, Li 2000), lattice models with dynamic copulas (Albanese et al. 2005, 2007, 2010), conditionally independent models (Vasicek 1987 and extensions), and the contagion correlation approach (Davis and Lo 1999, Jarrow and Yu 2001). New insights on the Gaussian copula, partly blamed for the global financial crisis 2007/2008 are given. We then discuss top-down approaches as Vasicek's 1987 large homogeneous portfolio (LHP), inducing correlation in Markov chain models (Hurd and Kuznetsov 2006a, 2006b, Schönbucher 2006), and the top-down contagion model of Giesecke et al 2009. This paper addresses the mathematical properties of the correlation approaches. A follow up paper will empirically test the correlation approaches using default data of the US banking sector before and during the 2007/2008 crisis