Extracting joint probability of default from CDS data

Systemic default risk -i.e. the risk of simultaneous default of multiple institutions- has caused great concern in recent past. However, the mea sure of systemic risk is not a trivial subject. The aim of this paper is to estimate the joint probability of default for couples of defaultable entities, belonging to different rating classes. Both bond and credit derivative markets convey information on the default probabilities. In particular, the price of Credit Default Swap (CDS) contracts involves counterparty risk i.e. the risk that the protection seller will fail to fulfill its obligations - usually either by failing to pay or by failing to deliver securities. The counterparty risk is reflected in the CDS price through the joint default probability of the reference entity and the protection seller. In this paper, applying a no-arbitrage argument, we extract forward looking joint default probabilities of institutions operating in the CDS market. The analysis of the dynamics of the joint default probability can provide clear signals of an increase in systemic risk and danger of contagion.