A note on the risk management of CDOs

The purpose of this note is to describe a risk management procedure applicable to options on large credit portfolios such as CDO tranches on iTraxx or CDX. Credit spread risk is dynamically hedged using single name defaultable claims such as CDS while default risk is kept under control thanks to diversification. The proposed risk management approach mixes ideas from finance and insurance and departs from standard approaches used in incomplete markets such as mean-variance hedging or expected utility maximisation. In order to ease the analysis and the exposure, default dates follow a multivariate Cox process.