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Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks


  • Damiano Brigo

    () (Imperial College, London, United Kingdom;
    Capco Institute)

  • Andrea Pallavicini

    () (Imperial College, London, United Kingdom;
    Banca IMI Milan, Italy)


The introduction of Central Clearing Counterparties (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 of about USD 2 trillions. In this paper, 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. This framework stems from our 2011 framework on credit, collateral and funding costs in Pallavicini et al. (Pallavicini, A., D. Perini and D. Brigo, 2011, Funding Valuation Adjustment: FVA consistent with CVA, DVA, WWR, Collateral, Netting and Re-hypothecation,, Mathematically, the inclusion of asymmetric borrowing and lending rates in the hedge of a claim, and a replacement closeout at default, lead to nonlinearities showing up in claim dependent pricing measures, aggregation dependent prices, nonlinear Partial Differential Equations (PDEs) and Backward Stochastic Differential Equations (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.

Suggested Citation

  • Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
  • Handle: RePEc:wsi:jfexxx:v:01:y:2014:i:01:n:s2345768614500019
    DOI: 10.1142/S2345768614500019

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    References listed on IDEAS

    1. Daniel Heller & Nicholas Vause, 2012. "Collateral requirements for mandatory central clearing of over-the-counter derivatives," BIS Working Papers 373, Bank for International Settlements.
    2. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    3. 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.
    4. Cyril Durand & Marek Rutkowski, 2013. "CVA for Bilateral Counterparty Risk under Alternative Settlement Conventions," Papers 1307.6486,
    5. Tomasz R. Bielecki & Marek Rutkowski, 2013. "Valuation and hedging of OTC contracts with funding costs, collateralization and counterparty credit risk: Part 1," Papers 1306.4733,, revised Jun 2013.
    6. Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767,
    7. Andrea Pallavicini & Damiano Brigo, 2013. "Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs," Papers 1304.1397,
    8. Rama Cont & Thomas Kokholm, 2013. "Central Clearing of OTC Derivatives: bilateral vs multilateral netting," Papers 1304.5065,
    9. Damiano Brigo & Agostino Capponi & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting," Papers 1101.3926,
    10. Manmohan Singh, 2011. "Making OTC Derivatives Safe—A Fresh Look," IMF Working Papers 11/66, International Monetary Fund.
    11. Lixin Wu, 2013. "CVA and FVA to Derivatives Trades Collateralized by Cash," Papers 1302.0465,
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    Cited by:

    1. Damiano Brigo & Cristin Buescu & Marco Francischello & Andrea Pallavicini & Marek Rutkowski, 2018. "Risk-neutral valuation under differential funding costs, defaults and collateralization," Papers 1802.10228,


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