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 main indices. Credit spread risks are dynamically hedged using single name credit default swaps 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, within a reference credit portfolio, follow a multivariate Cox process. In such a framework, thanks to the no contagion property, i.e. default of a name does not trigger jumps in the credit spreads of the survivors and to the no simultaneous default property, i.e. the probability of joint defaults equals zero, we show that the hedging error can be kept under control. More specifically, by dynamically hedging of portfolio of single name credit default swaps, the hedging residual is bounded in ${\mathcal{L}^1}$. Moreover, the associated strategy corresponds to the mean variance hedging of a pseudo CDO tranche, where the actual portfolio loss is replaced by its projection on the background filtration.