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Affine multiple yield curve models

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  • Christa Cuchiero
  • Claudio Fontana
  • Alessandro Gnoatto

Abstract

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 Heath–Jarrow–Morton modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded overnight indexed swap 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 multicurve 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.

Suggested Citation

  • Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:2:p:568-611
    DOI: 10.1111/mafi.12183
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    Cited by:

    1. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    2. Sandrine Gumbel & Thorsten Schmidt, 2020. "Machine learning for multiple yield curve markets: fast calibration in the Gaussian affine framework," Papers 2004.07736, arXiv.org, revised Apr 2020.
    3. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    4. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    5. 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.
    6. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2019. "Multiple yield curve modelling with CBI processes," Papers 1911.02906, arXiv.org, revised Oct 2020.
    7. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2018. "Multiple curve L\'evy forward price model allowing for negative interest rates," Papers 1805.02605, arXiv.org.
    8. Claudio Fontana, 2022. "Caplet pricing in affine models for alternative risk-free rates," Papers 2202.09116, arXiv.org, revised Jan 2023.
    9. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2019. "Multiple curve Lévy forward price model allowing for negative interest rates," Post-Print hal-03898912, HAL.
    10. Markus Hess, 2020. "A pure-jump mean-reverting short rate model," Papers 2006.14814, arXiv.org.
    11. Yangfan Zhong, 2018. "LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-38, June.
    12. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    13. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    14. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org, revised Nov 2024.
    15. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    16. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882, arXiv.org, revised Dec 2019.
    17. Sandrine Gümbel & Thorsten Schmidt, 2020. "Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework," Risks, MDPI, vol. 8(2), pages 1-18, May.
    18. Yangfan Zhong & Yanhui Mi, 2018. "Pricing in-arrears caps and ratchet caps under LIBOR market model with multiplicative basis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-31, September.
    19. Joel P. Villarino & 'Alvaro Leitao & Jos'e A. Garc'ia-Rodr'iguez, 2022. "Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk," Papers 2210.02175, arXiv.org.
    20. Claudio Fontana & Eckhard Platen & Stefan Tappe, 2024. "Real-world models for multiple term structures: a unifying HJM framework," Papers 2411.01983, arXiv.org.
    21. Dorota Toczydlowska & Gareth W. Peters, 2018. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics," Econometrics, MDPI, vol. 6(3), pages 1-45, July.

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