Yang, Jingping, Tom Hurd, and Xuping Zhang, "Saddlepoint Approximation Method for Pricing CDOs", Journal of Computational Finance, Vol. 10, No. 1, (Fall 2006), pp. 1-20.
Abstract: A critical issue in the credit risk industry is the accurate, efficient and robust pricing of collateralized debt obligations (CDO) in a variety of mathematical models. These and many similar basket default products are very complex, due to characteristics of the large number of individual firms upon which they depend. Despite this complexity and because of their versatility, such products have become popular in the market. A central difficulty which arises in most models of CDOs is the efficient computation of conditional default loss distributions. Since exact computation is feasible only in highly symmetric situations, it is necessary to have a variety of acceptable approximation schemes. The present paper explores one general method, the saddlepoint approximation, and shows that it gives promising results when compared with simpler methods.
Keywords: large deviations, credit risk, basket credit derivative, collateralized debt obligation, tranche.