IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1304.1397.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1304.1397
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    3. Masaaki Kijima & Keiichi Tanaka & Tony Wong, 2009. "A multi-quality model of interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 133-145.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Alfeus, Mesias & Grasselli, Martino & Schlögl, Erik, 2020. "A consistent stochastic model of the term structure of interest rates for multiple tenors," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    4. Chiara Sabelli & Michele Pioppi & Luca Sitzia & Giacomo Bormetti, 2014. "Multi-curve HJM modelling for risk management," Papers 1411.3977, arXiv.org, revised Oct 2015.
    5. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    6. 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.
    7. repec:uts:finphd:41 is not listed on IDEAS
    8. 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.
    9. Alessandro Gnoatto & Nicole Seiffert, 2020. "Cross Currency Valuation and Hedging in the Multiple Curve Framework," Working Papers 03/2020, University of Verona, Department of Economics.
    10. Filipović, Damir & Trolle, Anders B., 2013. "The term structure of interbank risk," Journal of Financial Economics, Elsevier, vol. 109(3), pages 707-733.
    11. 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.
    12. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    13. 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.
    14. Nikolaos Karouzakis & John Hatgioannides & Kostas Andriosopoulos, 2018. "Convexity adjustment for constant maturity swaps in a multi-curve framework," Annals of Operations Research, Springer, vol. 266(1), pages 159-181, July.
    15. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    16. The Anh Nguyen & Frank Thomas Seifried, 2015. "The Multi-Curve Potential Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-32, November.
    17. Marco, Bianchetti & Mattia, Carlicchi, 2012. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," MPRA Paper 42248, University Library of Munich, Germany.
    18. Yang Chang, 2014. "A Consistent Approach to Modelling the Interest Rate Market Anomalies Post the Global Financial Crisis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 18, July-Dece.
    19. Gerhart, Christoph & Lütkebohmert, Eva, 2020. "Empirical analysis and forecasting of multiple yield curves," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 59-78.
    20. Jean-Paul Laurent & Philippe Amzelek & Joe Bonnaud, 2014. "An overview of the valuation of collateralized derivative contracts," Review of Derivatives Research, Springer, vol. 17(3), pages 261-286, October.
    21. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org, revised Nov 2024.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1304.1397. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.