Modeling collateralized debt obligations: A copula approach
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This master thesis gives an introduction to collateralized debt obligations (CDOs), and presents three models for pricing CDO tranches - The Vasicek model, which is considered to be the standard market model, the double NIG copula model introduced by Kalemanova et al. (2005), and the multivariate NIG model, which to our knowledge never before has been used for modeling credit derivatives. For all models, all obligors are assumed to have the same default probability, the same loss given default, and the same pairwise correlation. With statistical notion, all random variables in the multivariate distribution that describes defaults are equal and exchangeable, which in turn is exploited in a large homogeneous portfolio approximation for the fraction of defaults in the CDO. Model parameters are estimated from CDS spreads and equity returns corresponding to the underlying obligors, and compared to market prices for a CDO on the CDX NA IG index. The models are also optimized to fit the market prices for three different error measures, of which one is introduced in this thesis. The double NIG copula model gives the best fit to market prices both for the estimated and the optimized parameters. Very different tranche prices for the double NIG copula model and the multivariate NIG model even though the margins in both models are the same, demonstrates the importance of the copula in such models.