Measuring the Dependence between Non-Gaussian Financial Assets Using Copulae : Risk Management, Option Pricing and Default Risk

This paper aims to provide an introductory review of copulae and their potential application finance, in particular in capturing the dependence between financial assets that follow non-gaussian distributions and hence for modelling credit risk, pricing options and portfolio design. We briefy review the failure of methods based on multivariate normality and where dependency is measured by correlation. Using a copula approach enables us to measure the different relationships that may exist between financial assets in different ranges of their behaviour- for instance do assets exhibit similar dependency patterns in the tails of their distributions as they do around their means? We review different measures of association and show that when these dependency measures can be expressed simply as functions of a copula they will be invariant to strictly monotone transformations of the random variables and hence the units in which we choose to express our data. The standard Pearson Correlation statistic is not in general invariant to scale changes in the data. We then discuss several statistical issues relating to the estimation of Copulae and their empirical application through both parametric and non parametric methods. An important issue lies in the statistical discrimination between copulae and we propose a encompassing framework based on simulation for discriminating between what are effectively separate statistical families. We then consider several applications, modelling default risk, tail dependence, quantile regression and portfolio design for non-gaussian assets