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The Multi-Curve Potential Model

Author

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  • THE ANH NGUYEN

    (Department of Mathematics, University of Kaiserslautern, 67663 Kaiserslautern, Germany)

  • FRANK THOMAS SEIFRIED

    (Department IV – Mathematics, University of Trier, Universitätsring 19, 54296 Trier, Germany)

Abstract

We develop a general class of multi-curve potential models for post-crisis interest rates. Our model features positive stochastic basis spreads, positive term structures, and analytic pricing formulae for interest rate derivatives. Making a quanto interpretation of LIBOR lending transactions, we use a multi-currency analogy to model multiple term structures and formulate a general, tractable model of multiple term structures. As a special case of our approach, we obtain a rational lognormal model that extends the original Flesaker–Hughston (1996) rational lognormal model to a multi-curve setting. In this setting we obtain analytic pricing formulae for caps and swaptions.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:07:n:s0219024915500491
    DOI: 10.1142/S0219024915500491
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    References listed on IDEAS

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    Cited by:

    1. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2019. "Multiple curve Lévy forward price model allowing for negative interest rates," Post-Print hal-03898912, HAL.
    2. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    3. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    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. Markus Hess, 2020. "A pure-jump mean-reverting short rate model," Papers 2006.14814, arXiv.org.
    6. Thomas Krabichler & Josef Teichmann, 2020. "The Jarrow & Turnbull setting revisited," Papers 2004.12392, arXiv.org.

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