Dynamic Hedging of Synthetic CDO Tranches: Bridging the gap between theory and practice

This paper intends to provide insights about the topical issue of risk managing synthetic CDOs. We stand in the grey zone between mathematical finance and financial econometrics, between academic and market practitioners approaches. We chose to first present two scholar models, each of them leading to perfect replication of CDO tranches with credit default swaps. Though they rely upon rather simplistic assumptions and are built upon different premises, they lead to similar hedge ratios. We also stress that the study of the hedging issue in these two approaches involves the same basic theoretical ingredients. We then discuss various problems related to the use of such models in designing hedging strategies for CDO tranches and back testing or assessing hedging performance. At this stage, it appears that model based hedging strategies do help in the risk management process. Even though correlation markets had to face serious tests, more data related to short term maturity equity tranche spreads and plain CDS are required to discriminate against competing modelling approaches.