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Affine multiple yield curve models


  • Christa Cuchiero
  • Claudio Fontana
  • Alessandro Gnoatto


We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multi-curve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.

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  • Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "Affine multiple yield curve models," Papers 1603.00527,, revised Feb 2017.
  • Handle: RePEc:arx:papers:1603.00527

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    References listed on IDEAS

    1. Eckhard Platen & Steffan Tappe, 2015. "Real-World Forward Rate Dynamics With Affine Realizations," Published Paper Series 2015-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    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.
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    5. Antonia Castaño-Martínez & Fernando López-Blázquez, 2005. "Distribution of a sum of weighted noncentral chi-square variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 397-415, December.
    6. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    7. Abdelkoddousse Ahdida & Aur'elien Alfonsi, 2010. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Papers 1006.2281,, revised Mar 2013.
    8. 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.
    9. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Post-Print hal-00491371, HAL.
    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. Don H. Kim, 2014. "Swaption Pricing In Affine And Other Models," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 790-820, October.
    12. Zorana Grbac & Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2014. "Affine LIBOR models with multiple curves: theory, examples and calibration," Papers 1405.2450,, revised Aug 2015.
    13. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137,, revised Apr 2011.
    14. Ruggero Caldana & Gianluca Fusai & Alessandro Gnoatto & Martino Grasselli, 2016. "General closed-form basket option pricing bounds," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 535-554, April.
    15. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
    16. Kenneth J. Singleton & Len Umantsev, 2002. "Pricing Coupon-Bond Options And Swaptions In Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 427-446.
    17. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
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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,
    2. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804,, revised Mar 2018.
    3. repec:gam:jecnmx:v:6:y:2018:i:3:p:34-:d:158660 is not listed on IDEAS
    4. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882,

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