In this article, we present pricing and risk management of synthetic CDOs and risk management of credit portfolios are closely related problems as both require modeling of the same distribution of portfolio loss. The valuation of a single tranche CDO is equivalent in complexity to the calculation of credit default VaR for a portfolio of single name entities, while the valuation of CDO² (CDO-squared) is a task closely related to the calculation of credit default VaR for a portfolio of single tranche CDOs. We examine the analytical techniques developed for credit portfolio problems with a view to CDO applications and find that the saddlepoint method works better than the alternatives, leading to a new, fast technique for CDO² pricing and hedging.
 

Authors: Alexander Antonov, Serguei Mechkov, and Timur Misirpashaev