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Affine LIBOR models with multiple curves: theory, examples and calibration

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  • Zorana Grbac
  • Antonis Papapantoleon
  • John Schoenmakers
  • David Skovmand

Abstract

We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine property is preserved under forward measures, which allows us to derive Fourier pricing formulas for caps, swaptions and basis swaptions. A model specification with dependent LIBOR rates is developed, that allows for an efficient and accurate calibration to a system of caplet prices.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1405.2450
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    References listed on IDEAS

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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    7. 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.
    8. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    9. 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.
    10. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    11. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2019. "Multiple curve Lévy forward price model allowing for negative interest rates," Post-Print hal-03898912, HAL.
    12. Alfred Wong & Jiayue Zhang, 2018. "Breakdown of covered interest parity: mystery or myth?," BIS Papers chapters, in: Bank for International Settlements (ed.), The price, real and financial effects of exchange rates, volume 96, pages 57-78, Bank for International Settlements.
    13. Alessandro Gnoatto & Nicole Seiffert, 2020. "Cross Currency Valuation and Hedging in the Multiple Curve Framework," Papers 2001.11012, arXiv.org, revised Mar 2021.
    14. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org.
    15. Antonis Papapantoleon & Robert Wardenga, 2016. "Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA," Papers 1607.03522, arXiv.org, revised Feb 2017.
    16. Markus Hess, 2019. "An Arithmetic Pure-Jump Multi-Curve Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-30, December.
    17. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2018. "Multiple curve L\'evy forward price model allowing for negative interest rates," Papers 1805.02605, arXiv.org.
    18. Markus Hess, 2020. "A pure-jump mean-reverting short rate model," Papers 2006.14814, arXiv.org.
    19. 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.
    20. Stefan Waldenberger & Wolfgang Muller, 2015. "Affine LIBOR models driven by real-valued affine processes," Papers 1503.00864, arXiv.org.
    21. 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.
    22. 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.

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