Modelling Dependent Financial Risks: Non-Gaussian Models and Copulas

Alexander McNeil

The material for this course is taken from the book "Quantitative Risk Management: Concepts, Techniques and Tools" by Alexander J. McNeil, Ruediger Frey and Paul Embrechts, Princeton University Press 2005. One of the main issues in the quantitative modelling of market and credit risk is capturing the multivariate behaviour of risk across a portfolio. Standard approaches relying on assumptions of multivariate normality and focussed on correlation matrices are known to have their deficiencies, particularly in characterizing the potential for extreme risk. In this course we will take a tour through relevant non-Gaussian models, treating, among other things, normal mixture models, generalized hyperbolic models and copula models for market risk factors as well as copula models and mixed Bernoulli models for credit risk. All ideas will be illustrated with examples in S-Plus using the author's QRMlib library.