Updated version forthcoming in the International Journal of Theoretical and Applied Finance

COUNTERPARTY RISK FOR CREDIT DEFAULT SWAPS impact of spread volatility and default correlation Damiano Brigo Fitch Solutions and Dept. of Mathematics, Imperial College 101 Finsbury Pavement, EC2A 1RS London. E-mail: damiano.brigo@fitchsolutions.com Kyriakos Chourdakis Fitch Solutions and CCFEA, University of Essex 101 Finsbury Pavement, EC2A 1RS London. E-mail: kyriakos.chourdakis@fitchsolutions.com

Abstract We consider counterparty risk for Credit Default Swaps (CDS) in presence of correlation between default of the counterparty and default of the CDS reference credit. Our approach is innovative in that, besides default correlation, which was taken into account in earlier approaches, we also model credit spread volatility. Stochastic intensity models are adopted for the default events, and defaults are connected through a copula function. We find that both default correlation and credit spread volatility have a relevant impact on the positive counterparty-risk credit valuation adjustment to be subtracted from the counterparty-risk free price. We analyze the pattern of such impacts as correlation and volatility change through some fundamental numerical examples, analyzing wrong-way risk in particular. Given the theoretical equivalence of the credit valuation adjustment with a contingent CDS, we are also proposing a methodology for valuation of contingent CDS on CDS.

AMS Classification Codes: 60H10, 60J60, 60J75, 62H20, 91B70 JEL Classification Codes: C15, C63, C65, G12, G13 Keywords: Counterparty Risk, Credit Valuation adjustment, Credit Default Swaps, Contingent Credit Default Swaps, Credit Spread Volatility, Default Correlation, Stochastic Intensity, Copula Functions, Wrong Way Risk. First version: May 16, 2008. This version: October 3, 2008

D. Brigo, K. Chourdakis, FitchSolutions, Counterparty risk valuation adjustment for CDS

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1 Introduction
We consider