Gaussian copula approach to assess risk and value of a credit risk tranche

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In the one factor Gaussian copula model, all the credits of the credit portfolio are correlated through a common market factor, and the common market factor is generated from the standard normal distribution.

This will create a continuous default probability distribution for each underlying credit under given correlation.

At present, the Gaussian copula approach is the most commonly used model in the structured credit market. Rating agencies and dealers rely on Monte Carlo simulation based on this model when they assess risk and value of a credit risk tranche.

Recently, some market participants have voiced their concerns about the heavy reliance on this model.

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Dependence modelling with copula functions is widely used in applications of financial risk assessment and actuarial analysis - for example in the pricing of collateralized debt obligations (CDOs). The methodology of applying the Gaussian copula to credit derivatives is said to be one of the reasons behind the global financial crisis of 2008–2009. Despite this perception, there are documented attempts of the financial industry, occurring before the crisis, to address the limitations of the Gaussian copula and of Copula functions more generally, specifically the lack of dependence dynamics and the poor representation of extreme events. The volume "Credit Correlation: Life After Copulas", published in 2007 by World Scientific, summarizes a 2006 conference held by Merrill Lynch in London where several practitioners attempted to propose models rectifying some of the copula limitations.

Recently, copula functions have been successfully applied to the database formulation for the reliability analysis of highway bridges and to various multivariate simulation studies in civil, mechanical and offshore engineering.