Pricing and hedging basket credit derivatives in the Gaussian copula

The static assumptions of the Gaussian copula model have long presented an obstacle to dynamic hedging of credit portfolio tranches. Here, Jean-David Fermanian and Olivier Vigneron combine the copula with a spread diffusion to derive hedging error as proportional to the gamma times the difference between implied and realised spread correlations, analogous to the classic Black-Scholes result. Consequently any basket derivative has a unique price and can be replicated using credit default swaps

Since the seminal paper of Li (2000), the Gaussian copula model has become the market standard of the structured credit derivatives world. By postulating a correlation structure for the default times of each issuer directly, this model allows the practitioner to price collateralised debt obligation (CDO) payouts and gives a simple solution for their risk management.

However, the choice of the pairwise correlations appears largely arbitrary and lacks a clear link with a concept of realised