Copulæ are an interesting mathematical tool to represent correlations between probability distributions. They can be used to represent complex dependencies in multivariate risk models, when more basic tools such as multivariate gaussian distributions are inappropriate. One commonly used application is sampling from correlated random variables.
Appropriate modelling of dependencies between model input variables is a very significant issue in risk models in a number of application areas. For example, an inappropriate (simplifying) assumption of gaussian dependencies between the risk of various financial instruments was one of the factors that led to the global financial crisis of 2008.
Illustrations of the concept are provided in finance, where the method first reached prominence. We also show applications in other areas, including insurance, management of natural hazards, and quality management in manufacturing.
This submodule is a part of the risk analysis module.
Copula and multivariate dependencies
We recommend the following sources of further information on this topic:
The Coursera course Financial Engineering and Risk Management (Columbia University)
Iversity course Monte Carlo Methods in Finance by Prof. Alberto Suárez, Universidad Autónoma de Madrid (including copulas)
Material by Prof. Arthur Charpentier (Université de Montreal), including his great blog, Freakonometrics
Teaching material by Prof. Paul Embrecht from ETH Zurich, an important researcher in the use of copula techniques in finance
Article ‘The Formula That Killed Wall Street’? The Gaussian Copula and the Material Cultures of Modelling by Donald MacKenzie and Taylor Spears