Risk Engineering

Copula methods
Modelling correlation between risks


A copula represents the dependency between two random variables 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.

Course material

Copula and multivariate dependencies

Lecture slides (PDF)
View on Slideshare

Applications are run using Python and the NumPy and SciPy libraries (these are all free software that you can install on your own computer).

Other resources

We recommend the following sources of further information on this topic:

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