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A general HJM framework for multiple yield curve modeling

Author

Listed:
  • Christa Cuchiero
  • Claudio Fontana

    (LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - ENSIIE - CNRS - Centre National de la Recherche Scientifique)

  • Alessandro Gnoatto

Abstract

We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between (normalized) FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure which allows for tractable valuation formulas for most interest rate derivatives. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.

Suggested Citation

  • Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Working Papers hal-01011752, HAL.
  • Handle: RePEc:hal:wpaper:hal-01011752
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01011752
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2018. "Multiple curve L\'evy forward price model allowing for negative interest rates," Papers 1805.02605, arXiv.org.
    2. Stephane Crepey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2015. "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments," Papers 1502.07397, arXiv.org.
    3. Thorsten Schmidt, 2016. "Shot-Noise Processes in Finance," Papers 1612.06616, arXiv.org.
    4. Tappe, Stefan, 2016. "Affine realizations with affine state processes for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2062-2091.
    5. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    6. repec:eee:ejores:v:263:y:2017:i:2:p:707-718 is not listed on IDEAS
    7. repec:gam:jrisks:v:6:y:2018:i:1:p:18-:d:134969 is not listed on IDEAS
    8. Giacomo Bormetti & Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2015. "Impact of Multiple Curve Dynamics in Credit Valuation Adjustments under Collateralization," Papers 1507.08779, arXiv.org, revised Sep 2015.
    9. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2015. "The Long-Term Swap Rate and a General Analysis of Long-Term Interest Rates," Papers 1507.00208, arXiv.org, revised Oct 2016.
    10. 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.
    11. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "Affine multiple yield curve models," Papers 1603.00527, arXiv.org, revised Feb 2017.
    12. Gallitschke, Janek & Seifried (née Müller), Stefanie & Seifried, Frank Thomas, 2017. "Interbank interest rates: Funding liquidity risk and XIBOR basis spreads," Journal of Banking & Finance, Elsevier, vol. 78(C), pages 142-152.
    13. repec:spr:annopr:v:266:y:2018:i:1:d:10.1007_s10479-017-2430-6 is not listed on IDEAS
    14. Stéphane Crépey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2016. "Rational multi-curve models with counterparty-risk valuation adjustments," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 847-866, June.
    15. Zorana Grbac & Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2014. "Affine LIBOR models with multiple curves: theory, examples and calibration," Papers 1405.2450, arXiv.org, revised Aug 2015.

    More about this item

    Keywords

    Multiple yield curves; HJM model; semimartingale; forward rate agreement; Libor rate; interest rate; affine processes;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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