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Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs

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  • Andrea Pallavicini
  • Damiano Brigo

Abstract

The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modelling, integrating the origination of different term structures with such effects. Under a number of assumptions on collateralization, wrong-way risk, gap risk, credit valuation adjustments and funding effects, including the treasury operational model, and via an immersion hypothesis, we are able to derive a synthetic master equation for the multiple term structure dynamics that integrates multiple curves with credit/funding adjustments.

Suggested Citation

  • Andrea Pallavicini & Damiano Brigo, 2013. "Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs," Papers 1304.1397, arXiv.org.
    • Handle: RePEc:arx:papers:1304.1397
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    References listed on IDEAS

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    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.
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    4. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    5. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    6. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811, arXiv.org, revised Dec 2012.
    7. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    8. Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767, arXiv.org.
    9. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    11. Tapking, Jens & Eisenschmidt, Jens, 2009. "Liquidity risk premia in unsecured interbank money markets," Working Paper Series 1025, European Central Bank.
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    Citations

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    Cited by:

    1. Laura Morino & Wolfgang J. Ruggaldier, 2014. "On multicurve models for the term structure," Papers 1401.5431, arXiv.org.
    2. Zorana Grbac & Laura Meneghello & Wolfgang J. Runggaldier, 2015. "Derivative pricing for a multi-curve extension of the Gaussian, exponentially quadratic short rate model," Papers 1512.03259, arXiv.org, revised Jun 2016.
    3. Chris Kenyon & Andrew Green, 2013. "Regulatory-Optimal Funding," Papers 1310.3386, arXiv.org, revised Aug 2014.
    4. Yannick Armenti & Stéphane Crépey, 2017. "Central Clearing Valuation Adjustment," Working Papers hal-01169169, HAL.
    5. Paul McCloud, 2019. "Repo convexity," Papers 1905.03316, arXiv.org.
    6. 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.
    7. Damiano Brigo & Qing Liu & Andrea Pallavicini & David Sloth, 2014. "Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes," Papers 1404.7314, arXiv.org.
    8. Giacomo Bormetti & Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2018. "Impact of multiple curve dynamics in credit valuation adjustments under collateralization," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 31-44, January.
    9. Fanelli, Viviana, 2017. "Implications of implicit credit spread volatilities on interest rate modelling," European Journal of Operational Research, Elsevier, vol. 263(2), pages 707-718.
    10. Michele Bonollo & Irene Crimaldi & Andrea Flori & Laura Gianfagna & Fabio Pammolli, 2016. "Assessing financial distress dependencies in OTC markets: a new approach using trade repositories data," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 30(4), pages 397-426, November.
    11. 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, arXiv.org.
    12. Fanelli, Viviana, 2016. "A defaultable HJM modelling of the Libor rate for pricing Basis Swaps after the credit crunch," European Journal of Operational Research, Elsevier, vol. 249(1), pages 238-244.
    13. 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, arXiv.org, revised Dec 2013.
    14. Yannick Armenti & St'ephane Cr'epey, 2015. "Central Clearing Valuation Adjustment," Papers 1506.08595, arXiv.org, revised Feb 2017.
    15. Nicola Moreni & Andrea Pallavicini, 2015. "FX Modelling in Collateralized Markets: foreign measures, basis curves, and pricing formulae," Papers 1508.04321, arXiv.org, revised Sep 2015.

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