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Multiple curve L\'evy forward price model allowing for negative interest rates

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  • Ernst Eberlein
  • Christoph Gerhart
  • Zorana Grbac

Abstract

In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the L\'evy Libor market model, it allows in a natural way for negative interest rates and has superb calibration properties even in the presence of extremely low rates. Moreover, the measure changes along the tenor structure are simplified significantly. These properties make it an excellent base for a post-crisis multiple curve setup. Two variants for multiple curve constructions are discussed. Time-inhomogeneous L\'evy processes are used as driving processes. An explicit formula for the valuation of caps is derived using Fourier transform techniques. Based on the valuation formula, we calibrate the two model variants to market data.

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  • Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2018. "Multiple curve L\'evy forward price model allowing for negative interest rates," Papers 1805.02605, arXiv.org.
    • Handle: RePEc:arx:papers:1805.02605
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    References listed on IDEAS

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    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    3. 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.
    4. 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.
    5. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    6. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    7. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
    8. Ernst Eberlein & Christoph Gerhart, 2018. "A multiple-curve Lévy forward rate model in a two-price economy," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 537-561, April.
    9. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
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    Cited by:

    1. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2019. "Multiple yield curve modelling with CBI processes," Papers 1911.02906, arXiv.org, revised Oct 2020.
    2. Grzegorz Krzy.zanowski & Ernesto Mordecki & Andr'es Sosa, 2019. "Zero Black-Derman-Toy interest rate model," Papers 1908.04401, arXiv.org, revised Jul 2020.
    3. Grzegorz Krzy.zanowski & Andr'es Sosa, 2020. "Performance analysis of Zero Black-Derman-Toy interest rate model in catastrophic events: COVID-19 case study," Papers 2007.00705, arXiv.org, revised Jul 2020.

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