Delta-hedging Correlation Risk?

The Gaussian copula model is essentially a static quotation device, and its use for hedging is, in principle, questionable. The Gaussian copula delta thus assumes a constant tranche correlation, whereas in practice this correlation is dynamic, and correlated in particular to the credit index. It might therefore be expected that a dynamic model of credit risk, able to capture at least part of the dependence between implied correlation and index spreads, should have better hedging performances. In this paper, we compare two deltas which can be used for hedging a CDO tranche by its credit index: the market or Gaussian copula delta, and the local intensity delta, where the latter refers to the delta in a local intensity default model of portfolio credit risk, recalibrated to the market every day. A theoretical analysis is illustrated by data analysis and backtesting hedging experiments based on both pre-crisis and crisis market data. We observe that hedging performance are comparable for crisis period associated with CDX Series 9 and 10. However, the local intensity delta fails to outperform the market delta in pre-crisis period associated with CDX Series 5, even if the local intensity model is a sound, dynamic model of credit risk, fitting the market over the full set of CDO tranches, as opposed to a static model and a per tranche fit in the case of the Gaussian copula model