Hedging issues for CDOs

This paper is a primer on the hedging and the risk management of CDO tranches. It intends to provide a global perspective on the current issues and refers to research papers for modelling and mathematical details. Though the basics of the risk management within the Gaussian copula model are not discussed, we review some issues which may eventually lead to the decline of the current market approach. We consider the computation of spread sensitivities in arbitrage-free dynamic models based on affine intensities and on Markov chains. We show that the one dimensional Markov chain for the aggregate loss process may viewed as the analogue for credit markets of the local volatility model in equity derivatives markets. In such a framework, CDO tranches can be fully replicated with the credit default swap index and a risk-free asset and the corresponding deltas correspond to a “sticky implied tree model”. Hedging issues related to tranchelets on standard indices or to CDO tranches on bespoke portfolios are dealt with. We also investigate some paths for the future, including the use of credit default swaps of different maturities to cope simultaneously with default and credit spread risks, local and asymptotic hedging approaches.