Abstract
The goal of this paper is to develop the dynamic alpha (α)-stable method for collateralized debt obligation (CDO) pricing based on the α-stable distributions, which will resolve the two issues caused by using traditional static factor copula method in the practice, which means when pricing CDOs, the traditional static factor Copula method does not only exhibit the correlation smile phenomenon which is not inconsistent with the model's assumption, but also cannot be used in pricing CDOs or credit portfolio derivatives for the underlying portfolio with different maturities. As the applications, we present calibration and empirical numerical results for iTraxx Europe Tranches quotes from the market data on March 30, 2007. Thus, our new method under the framework of the dynamic α-stable model is the way for CDO pricing in the practice, and should be useful for the risk management in the practice too.
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