Pricing and Hedging of Cdo-squared Tranches by Using a One Factor Lévy Model

This paper provides a comparison of the exponential copula Lévy model with the classical Gaussian copula model for the pricing of CDO-squared tranches. Several approximations of the recursive approach are considered: a full Monte Carlo approximation, a multivariate Normal approximation of the joint inner CDO loss distribution and a multivariate Poisson approximation of the joint number of defaults affecting the inner CDOs. More particularly, a sensitivity analysis is carried out for three particular days characterised by a low, medium and high value of the quoted iTraxx and CDX index spreads. Moreover, this paper features a comparison of the exponential Lévy and Gaussian Deltas under the multivariate Normal approximation for a period extended from the 20 of September 2007 until the 13 of February 2008. The Deltas are computed with respect to a weighted and unweighted version of the CDS pool as well as with respect to another CDO-squared tranche. ∗K.U.Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven, Belgium. E-mail: [email protected] †KBC Group, Value and Risk Management Department. E-mail: [email protected] ‡K.U.Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven, Belgium. E-mail: [email protected]