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Counterparty Risk for Credit Default Swaps: Impact of spread volatility and default correlation

by Damiano Brigo of FitchSolutions & Imperial College, and
Kyriakos Chourdakis of FitchSolutions & University of Essex

October 3, 2008

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.

JEL Classification: C15, C63, C65, G12, G13.

AMS Classification: 60H10, 60J60, 60J75, 62H20, 91B70.

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.

Published in: International Journal of Theoretical and Applied Finance, Vol. 12, No. 7, (November 2009) pp. 1007-1026.

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