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CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation Approach


  • Damiano Brigo
  • Andrea Pallavicini


The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collateralization, showing concrete examples for interest rate swaps. Mathematically, the inclusion of asymmetric borrowing and lending rates in the hedge of a claim lead to nonlinearities showing up in claim dependent pricing measures, aggregation dependent prices, nonlinear PDEs and BSDEs. This still holds in presence of CCPs and CSA. We introduce a modeling approach that allows us to enforce rigorous separation of the interconnected nonlinear risks into different valuation adjustments where the key pricing nonlinearities are confined to a funding costs component that is analyzed through numerical schemes for BSDEs. We present a numerical case study for Interest Rate Swaps that highlights the relative size of the different valuation adjustments and the quantitative role of initial and variation margins, of liquidity bases, of credit risk, of the margin period of risk and of wrong way risk correlations.

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  • Damiano Brigo & Andrea Pallavicini, 2014. "CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation Approach," Papers 1401.3994,
  • Handle: RePEc:arx:papers:1401.3994

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    References listed on IDEAS

    1. N. Moreni & A. Pallavicini, 2014. "Parsimonious HJM modelling for multiple yield curve dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 199-210, February.
    2. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    3. Andrea Pallavicini & Damiano Brigo, 2013. "Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs," Papers 1304.1397,
    4. Tapking, Jens & Eisenschmidt, Jens, 2009. "Liquidity risk premia in unsecured interbank money markets," Working Paper Series 1025, European Central Bank.
    5. Daniel Heller & Nicholas Vause, 2012. "Collateral requirements for mandatory central clearing of over-the-counter derivatives," BIS Working Papers 373, Bank for International Settlements.
    6. Damiano Brigo & Andrea Pallavicini, 2013. "CCPs, Central Clearing, CSA, Credit Collateral and Funding Costs Valuation FAQ: Re-hypothecation, CVA, Closeout, Netting, WWR, Gap-Risk, Initial and Variation Margins, Multiple Discount Curves, FVA?," Papers 1312.0128,, revised Dec 2013.
    7. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811,, revised Dec 2012.
    8. Tomasz R. Bielecki & Stéphane Crépey & Monique Jeanblanc & Marek Rutkowski, 2008. "Defaultable Options In A Markovian Intensity Model Of Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 493-518.
    9. Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767,
    10. Bergman, Yaacov Z, 1995. "Option Pricing with Differential Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 475-500.
    11. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
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    Cited by:

    1. repec:wsi:jfexxx:v:01:y:2014:i:01:n:s2345768614500081 is not listed on IDEAS
    2. Wujiang Lou, 2015. "MVA Transfer Pricing," Papers 1512.07337,, revised Jul 2016.
    3. Stéphane Crépey & Shiqi Song, 2014. "BSDEs of Counterparty Risk," Working Papers hal-01088941, HAL.

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