This book is a compilation of articles that have been published in Invesco’s Risk & Reward publication. The focus of these articles were twofold. First, the inadequacies of the conventional tools are outlined. In particular, the assumption of independent identical normally distributed returns is ill-suited to the realities of the financial markets. Second, complex methodologies, such as risk modelling using Copulas, as well as practice-oriented means of risk approximation are explained from a conceptional point of view, such to provide the reader with a basic understanding of these techniques. The aim throughout is to modify distribution assessments in such a way to render Value-at-Risk and Expected Shortfall more useful in practical risk management. A German version of this book has been made available, too. Aside from the other channels, these books can directly be ordered from the publisher by following the link as shown by the cover image on the top right.


The content of the book is structured as:

  • First Preface
  • Second Preface
  • Risk modelling and extreme value theory
  • Distributions for modelling of financial market time series
  • Conditional volatility modelling
  • Concepts and measures for detecting relations between risk factors
  • The concept of a copula
  • Alternative risk measures in the portfolio context
  • The copula-GARCH procedure
  • Appendix
  • List of Figures
  • List of Tables
  • Bibliography
  • The author
  • Portrait of the Company


German version: Bernhard Pfaff, Modellierung von Einzel- und Portfoliorisiken, Fat Tails, Volatilitäsbündelung und Copulae, Frankfurter Allgemeine Buch, 2010, Frankfurt am Main, ISBN 978-3-89981-227-5.

English version: Bernhard Pfaff, Modelling Financial Risks, Fat Tails, Volatility Clustering and Copulae, Frankfurter Allgemeine Buch, 2010, Frankfurt am Main, ISBN 978-3-89981-229-9.