Calibrating risk‐neutral default correlation

The implementation of credit risk models has largely relied either on the use of historical default dependence, as proxied by the correlation of equity returns, or on risk neutral equicorrelation, as extracted from CDOs. Contrary to both approaches, the purpose of this paper is to infer risk neutral dependence from CDS data, taking counterparty risk into consideration and avoiding equicorrelation. The impact of risk neutral correlation on the fees of some higher dimensional credit derivatives is also explored.

Copula functions are used in order to capture dependency. An application to market data is provided.

Both in the FtD and CDO cases, using (the correct) risk neutral measure instead of equity dependency has the same effect as the adoption of a copula with tail dependency instead of a Gaussian one. This should be important for those who resort to copulas in credit derivative pricing.

As far as is known, several attempts have been made in order to compare the behavior of different copulas in derivative pricing; however, no attempt has been made in order to extract risk neutral dependence without using the equicorrelation assumption. Therefore no attempt has been made to understand which copula features could proxy for risk neutrality, whenever risk neutral dependency cannot be inferred (for instance because CDS involving that name are not actively traded)