Dynamic Hedging of Portfolio Credit Derivatives

Abstract:     
As shown by the recent turmoil in credit markets, much remains to be done for the proper risk management of credit derivatives. In particular, the static copula-based models commonly used for pricing portfolio credit derivatives appear to be inappropriate for hedging and risk management. We study hedging of index CDO tranches with the underlying index default swap using various portfolio loss models which account for default contagion and spread risk. Numerical results obtained from models calibrated to iTraxx Europe data reveal significant differences in hedge ratios across models and show, unlike what had been previously suggested in the literature by comparing copula-based models, that hedging strategies are subject to substantial model risk. An empirical analysis based on recent market data shows that strategies based on delta-hedging of spread movements have poorly performed during the 2007-2008 sub prime crisis, while variance-minimizing hedges led to significantly smaller losses. Our empirical study also reveals that, while significantly large moves - "jumps" - do occur in index spreads, these jumps do not necessarily occur on default dates of index constituents, an observation which contradicts the intuition conveyed by some recently proposed credit risk models.

Keywords: hedging, portfolio credit derivatives, index default swaps, collateralized debt obligations, top-down credit risk models, default contagion, spread risk, sensitivity-based hedging, risk minimization

JEL Classifications: G13, G12

Working Paper Series