Synthetic Collateralized Debt Obligations and Kth to Default Swaps Valuation Using Copula Model

In this paper, I present an approach for valuing credit default swap (CDS), tranches of synthetic collateralized debt obligations and kth to default swaps. One-factor gaussian copula model is utilized to model default correlation for each pair of companies. In this research, I analyze the effect of different hazard rates and different default correlation between each pair of names on the spread to buy protection for multi-name credit products. The findings in the valuation of a tranche of a CDO show that if the correlation is low, the junior equity tranche is very risky and the senior tranches are very safe. As the default correlation increases, the junior tranches become less risky and the senior tranches become more risky. The valuation of kth to default swaps also shows that as the hazard rate increases, the spread of all swaps increases. Also, increasing the correlations between all firms while holding the hazard rate constant lowers the cost of protection in kth to default CDS if k is small and increases it if k is large.