9. Modelling Dependence

  1. Bernhard Pfaff

Published Online: 30 OCT 2012

DOI: 10.1002/9781118477144.ch9

Financial Risk Modelling and Portfolio Optimization with R

Financial Risk Modelling and Portfolio Optimization with R

How to Cite

Pfaff, B. (2012) Modelling Dependence, in Financial Risk Modelling and Portfolio Optimization with R, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781118477144.ch9

Author Information

  1. Invesco Global Strategies, Germany

Publication History

  1. Published Online: 30 OCT 2012
  2. Published Print: 28 DEC 2012

ISBN Information

Print ISBN: 9780470978702

Online ISBN: 9781118477144



  • copula modelling;
  • financial markets;
  • financial risk modelling;
  • GARCH-copula model;
  • Pearson’s correlation coefficient;
  • R package;
  • rank correlation


The potential losses arising from holding a position in an asset were interpreted as a random variable and unconditional as well as conditional risk measures were derived. This chapter addresses the financial risk modelling in the context of multiple financial instruments. It introduces the correlation coefficient between two assets and investigates its appropriateness as a measure of dependence between two assets. The chapter discusses alternative measures of dependence, namely the use of rank correlations and the concept of the copula. It introduces two further concepts for capturing the dependence between risk factors, namely, concordance and tail dependence. A synopsis of the R packages that specifically include copula modelling is also provided. Finally, the chapter provides empirical applications of copulae. In particular, a GARCH-copula model is proposed for measuring the market risk of a portfolio.

Controlled Vocabulary Terms

copula; GARCH model; rank correlation