Pricing Portfolio Credit Derivatives by Means of Evolutionary Algorithms

Collateralized Debt Obligations (CDOs) are the most prominent example of portfol- related credit derivatives. They make it possible to diversify and transfer credit risk by pooling and redistributing the risks of an underlying portfolio of defaultable assets. It comes as no surprise that the dependence structure of portfolio assets is crucial for the valuation of CDO tranches. The standard market model is the Gaussian copula model, which uses only one parameter to summarize the correlations of default times in the underlying credit portfolio. Comparable with the volatility smile from option pricing, this simpli?cation leads to an implied correlation smile when the model is confronted with market data. There is a growing interest in literature searching for solutions of this problem. Dr. Svenja Hager contributes to this literature by extending the Gaussian copula model, allowing for a heterogeneous speci?cation of the dependence structure of the underlying portfolio. She shows that heterogeneous correlation matrices are able to explain the correlation smile. Based on this discovery, she develops a method to ?nd the implied correlation matrix which optimally reproduces the observed tranche spreads of a CDO structure. To overcome the complexity of the resulting optimization problems, Evo- tionary Algorithms are applied successfully. This monographputs anew complexion onthe standardmarket modelandshouldthe- fore be recognized for its substantial contribution in this fascinating ?eld of research on credit derivatives.