Pricing portfolio credit derivatives by means of evolutionary algorithms

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Collateralized Debt Obligations (CDOs) exemplify portfolio-related credit derivatives, enabling the diversification and transfer of credit risk through the pooling of defaultable assets. The dependence structure of these assets is vital for valuing CDO tranches, with the Gaussian copula model being the standard market approach. This model simplifies correlations of default times using a single parameter, leading to an implied correlation smile when matched against market data, akin to the volatility smile in option pricing. Recent literature has sought solutions to this issue, and Dr. Svenja Hager's work significantly contributes by extending the Gaussian copula model to allow for a heterogeneous specification of the dependence structure. She demonstrates that heterogeneous correlation matrices can effectively explain the correlation smile. Building on this insight, she devises a method to identify the implied correlation matrix that best replicates observed tranche spreads in a CDO structure. To tackle the complexity of the optimization challenges, she successfully employs Evolutionary Algorithms. This monograph offers a fresh perspective on the standard market model, marking a substantial advancement in the research of credit derivatives.