Counterparty Risk and Contingent CDS Valuation Under Correlation Between Interest-Rates and Default

We consider counterparty risk for interest rate payoffs in presence of correlation between the default event and interest rates. The previous analysis of Brigo and Masetti (2006), assuming independence, is further extended to interest rate payoffs different from simple swap portfolios. A stochastic intensity model with possible jumps is adopted for the default event. We find that correlation between interest-rates and default has a relevant impact on the positive adjustment to be subtracted from the default free price to take into account counterparty risk. We analyze the pattern of such impacts as product characteristics and tenor structures change through some fundamental numerical examples. We find the counterparty risk adjustment to decrease with the correlation for receiver payoffs, while the analogous adjustment for payer payoffs increases. The impact of correlation decreases when the default probability increases. Finally, our analysis applies naturally also to Contingent Credit Default Swaps