Aug
17

## Copula simulation and estimation

Copula is widely used for multi-variate modeling, especially when the underlying marginal distributions are not the same, generally speaking, Copula has at least the following application:

• Copulas provide us with a deeper understanding of dependence as such.

• Many dependence concepts, orderings and measures of association depend on H only through C and are in other words margin-free.

• Copulas allow us to easily construct (and simulate from) multivariate distributions with given univariate margins. This fact is particularly useful for stress testing.

• Multivariate data can be modeled in two separate stages: The univariate marginals can be handled first and their dependence structure thereafter. This comes in especially handy when we either already have some information about the margins (e.g. in the bottom-up approach in risk management) or if finding appropriate marginal distributions is difficult. In the latter case, we can model the margins nonparametricaly and use a parametric copula model to describe their dependence.

......

Below is the matlab file for Copula simulation and estimation, enjoy.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=15449

wiki(Copula)

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• Copulas provide us with a deeper understanding of dependence as such.

• Many dependence concepts, orderings and measures of association depend on H only through C and are in other words margin-free.

• Copulas allow us to easily construct (and simulate from) multivariate distributions with given univariate margins. This fact is particularly useful for stress testing.

• Multivariate data can be modeled in two separate stages: The univariate marginals can be handled first and their dependence structure thereafter. This comes in especially handy when we either already have some information about the margins (e.g. in the bottom-up approach in risk management) or if finding appropriate marginal distributions is difficult. In the latter case, we can model the margins nonparametricaly and use a parametric copula model to describe their dependence.

......

Below is the matlab file for Copula simulation and estimation, enjoy.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=15449

wiki(Copula)

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I was wondering if you have some code which I can use as an example, for the joint probability density from the combination of two probability density in the form of marginal probabilities?

The variables are dependant, with a known correlation function. I was thinking something using copulas is possible.

gr.

sim