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Bilateral Credit Valuation Adjustment for Large Credit Derivatives Portfolios

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  • Lijun Bo
  • Agostino Capponi

Abstract

We obtain an explicit formula for the bilateral counterparty valuation adjustment of a credit default swaps portfolio referencing an asymptotically large number of entities. We perform the analysis under a doubly stochastic intensity framework, allowing for default correlation through a common jump process. The key insight behind our approach is an explicit characterization of the portfolio exposure as the weak limit of measure-valued processes associated to survival indicators of portfolio names. We validate our theoretical predictions by means of a numerical analysis, showing that counterparty adjustments are highly sensitive to portfolio credit risk volatility as well as to default correlation.

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  • Lijun Bo & Agostino Capponi, 2013. "Bilateral Credit Valuation Adjustment for Large Credit Derivatives Portfolios," Papers 1305.5575, arXiv.org.
    • Handle: RePEc:arx:papers:1305.5575
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    References listed on IDEAS

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    1. T. R. Bielecki & S. Crépey & M. Jeanblanc & B. Zargari, 2012. "Valuation And Hedging Of Cds Counterparty Exposure In A Markov Copula Model," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 4, pages 75-113, World Scientific Publishing Co. Pte. Ltd..
    2. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    3. Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
    4. Alain BÉlanger & Steven E. Shreve & Dennis Wong, 2004. "A General Framework For Pricing Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 317-350, July.
    5. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
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    Cited by:

    1. Tetsuya Adachi & Takumi Sueshige & Toshinao Yoshiba, 2019. "Wrong-way Risk in Credit Valuation Adjustment of Credit Default Swap with Copulas," IMES Discussion Paper Series 19-E-01, Institute for Monetary and Economic Studies, Bank of Japan.
    2. Tomoyuki Ichiba & Michael Ludkovski & Andrey Sarantsev, 2019. "Dynamic contagion in a banking system with births and defaults," Annals of Finance, Springer, vol. 15(4), pages 489-538, December.
    3. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    4. Konstantinos Spiliopoulos & Jia Yang, 2018. "Network effects in default clustering for large systems," Papers 1812.07645, arXiv.org, revised Feb 2020.
    5. Kim, Jinbeom & Leung, Tim, 2016. "Pricing derivatives with counterparty risk and collateralization: A fixed point approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 525-539.
    6. Bo, Lijun & Capponi, Agostino, 2015. "Counterparty risk for CDS: Default clustering effects," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 29-42.
    7. David Xiao, 2023. "Default Process Modeling and Credit Valuation Adjustment," Papers 2309.03311, arXiv.org.
    8. Feinstein, Zachary & Sojmark, Andreas, 2021. "Short communication: dynamic default contagion in heterogeneous interbank systems," LSE Research Online Documents on Economics 123789, London School of Economics and Political Science, LSE Library.
    9. Ding, Kailin & Ning, Ning, 2021. "Markov chain approximation and measure change for time-inhomogeneous stochastic processes," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    10. Lee, David, 2023. "Default Forecasting and Credit Valuation Adjustment," MPRA Paper 118578, University Library of Munich, Germany.
    11. Agostino Capponi & Xu Sun & David D. Yao, 2020. "A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1127-1152, August.
    12. Lixin Wu & Dawei Zhang, 2020. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-24, February.
    13. Irena Barjav{s}i'c & Stefano Battiston & Vinko Zlati'c, 2023. "Credit Valuation Adjustment in Financial Networks," Papers 2305.16434, arXiv.org.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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