A Comparative Analysis of Correlation Approaches in Finance

Abstract

Although volatility is the key parameter for plain vanilla option pricing, many kinds of credit derivatives and exotic options involve multiple risk factors, so correlations must also be modeled. Different types of derivatives entail different types of correlation, from the basic Pearson correlation used in ordinary futures hedging and equity portfolio calculations, to copula methods that allow a wide range of tail dependence properties, to the ubiquitous Gaussian copula of credit risk modeling. Models of stochastically time-varying correlations have been developed, and for the correlation structure within a credit portfolio that may contain thousands of individual loans, top-down methods like Vasicek’s large homogeneous portfolio approximation may be required. This article provides a comprehensive review of the many correlation concepts and models that are increasingly necessary for modern derivatives researchers.