On Break-Even Correlation : The Way to Price Structured Credit Derivatives by Replication

We consider the pricing of European structured products under a 'static' framework, particularly the Gaussian copula model (GCM). Being hedged continuously against individual spread moves with single name Credit Default Swaps, we calculate the associated replication errors. Therefore, we introduce the concept of 'break-even' correlation (and more generally 'break-even' correlation matrix), that allow a perfect hedging under the GCM if and only if the underlying single names follow a particular family of dynamics, and when no jump-to-default events occur. We exhibit a class of Merton-type models that are consistent with this result. We explain why the GCM has not a lot of competitors among one-period static models, except the Clayton copula. Finally, we illustrate the theory by the empirical features of break-even correlations on true quotes (standard credit indices) and on simulated spread trajectories