Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis

People Research Publications Teaching

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Bilateral Counterparty Risk Valuation of CDS contracts with Simultaneous Defaults

Masterarbeit Mathematik

Supervision

• Prof. Dr. Matthias Ehrhardt
• Prof. Dr. Michael Günther

Description

In this thesis we analyze the general risk-neutral valuation for counterparty risk embedded in a Credit Default Swap (CDS) contract by adapting the recent findings of Brigo and Capponi to allow for simultaneous defaults among the two parties and the underlying reference credit, while the counterparty risk is considered bilaterally. For the default intensities we employ a Markov copula model allowing for the possibility of a simultaneous default. The dependence between defaults of three names in a CDS contract and the wrong-way risk will thus be represented by the possibility of simultaneous defaults.

Using our numerical results we investigate the effect of considering simultaneous defaults on the counterparty risk valuation of a CDS contract. Finally, we study a CDS contract between Royal Dutch Shell and British Airways based on Lehman Brothers applying this methodology, illustrating the bilateral adjustments with the possibility of simultaneous defaults in concrete crisis situations.

Keywords

Credit Default Swaps, Counterparty Risk, Risk-neutral Credit Valuation Adjustment, Default Intensity, Default Correlation, Simultaneous Default, Markov Copula Model.

References:

1. S. Assefa, T.R. Bielecki, S. Crépey, M. Jeanblanc, CVA computation for counterparty risk assessment in credit portfolios, In: Credit Risk Frontiers: Subprime Crisis, Pricing and Hedging, CVA, MBS, Ratings, and Liquidity. Bloomberg, 2011.
2. T.R. Bielecki, A. Cousin, S. Crépey, A. Herbertsson, Pricing and Hedging Portfolio Credit Derivatives in a Bottom-up Model with Simultaneous Defaults, Working Paper, 2011.
3. D. Brigo, A. Capponi, Bilateral Counterparty Risk Valuation with Stochastic Dynamical Models and Application to Credit Default Swaps, Working Paper, 2009.
4. T.R. Bielecki, I. Cialenco, I. Iyigunler, Counterparty Risk and the Impact of Collateralization in CDS contracts, Working Paper, 2011.
5. D. Brigo and K. Chourdakis, Counterparty Risk for Credit Default Swaps: Impact of spread volatility and default correlation, Int. J. Theoret. Appl. Fin. 12 (2009) 1007-1026.
6. D. Brigo, A. Pallavicini, V. Papatheodorou, Arbitrage-Free Valuation of Bilateral Counterparty Risk for Interest Rate Products: Impact of Volatilities and Correlations, Int. J. Theoret. Appl. Fin. 14 (2011), 773-802.
7. D. Brigo, C. Buescu, M. Morini, Counterparty Risk Pricing: Impact of closeout and First-To-Default Times, Int. J. Theoret. Appl. Fin. 15 (2012), 1250039 (23 pages).
8. D. Brigo, L. Cousot, The Stochastic Intensity SSRD Model Implied Volatility Patterns for Credit Default Swap Options and the Impact of Correlation, Int. J. Theoret. Appl. Fin. 9 (2006), 315-339.
9. D. Brigo, A. Capponi, Bilateral counterparty risk with application to CDSs, Risk Magazine, March 2010.
10. T.R. Bielecki, S. Crépey, M. Jeanblanc, B. Zargari, Valuation and Hedging of CDS Counterparty Exposure in A Markov Copula Model, Int. J. Theoret. Appl. Fin. 15 (2012), 1250004.
11. D. Brigo, F. Mercurio, Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit, Second Edition, Springer Verlag, 2006.
12. L. Teng, M. Ehrhardt, M. Günther, Bilateral Counterparty Risk Valuation of CDS contracts with Simultaneous Defaults, Preprint 13/01, January 2013.