Encyclopedia of Financial Models III

Copulas

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair-Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

CHRISTIAN MENN, Dr. rer. pol.

Managing Partner, RIVACON

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Understanding dependences or functional links between variables is a key theme in financial modeling. In general terms, functional dependences are represented by dynamic models. Many important models are linear models whose coefficients are correlations coefficients. In many instances in financial modeling, it is important to arrive at a quantitative measure of the strength of dependencies. The correlation coefficient provides such a measure. In many instances, however, the correlation coefficient might be misleading. In particular, there are cases of nonlinear dependencies that result in a zero correlation coefficient. From the point of view of financial modeling, this situation is particularly dangerous as it leads to substantially underestimated risk. Different measures of dependence have been proposed, in particular copula functions.

Correlation is a widespread concept in financial modeling and stands for a measure of dependence between random variables. However, this term is very often incorrectly used to mean any notion of dependence. Actually correlation is one particular measure of dependence among many. In the world of multivariate normal ...