CVA and the equivalent bond

Riccardo Rebonato, Mike Sherring and Ronnie Barnes investigate whether it is possible to model the credit valuation adjustment (CVA) by means of an equivalent bond, and if the regulatory Method 1 constitutes an acceptable approximation. They conclude that any equivalent-bond formulation (of the form proposed by the regulators) fundamentally misrepresents the CVA sensitivity to changes in credit spreads, that Method 1 is not an optimal equivalent-bond approximation, and that the International Swaps and Derivatives Association suggestion is compatible with a risk-sensitive capital model

A number of different suggestions have been proposed to come up with a simple, yet risk-sensitive, capital charge to cover changes in the mark-to-market value of the credit valuation adjustment (CVA) arising from counterparty exposures. In particular, regulators have proposed mimicking in a simple way the behaviour of the CVA exposure to changes in credit spreads by using an equivalent risky discount bond (the equivalent-bond approach). The industry has put forward counterproposals with