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Multiple Yield Curve Modelling with CBI Processes

Author

Listed:
  • Claudio Fontana

    (Department of Mathematics “Tullio Levi Civita”, University of Padova)

  • Alessandro Gnoatto

    (Department of Economics (University of Verona))

  • Guillaume Szulda

    (Laboratoire de Probabilités, Statistique et Mode ́lisation (LPSM), Paris Diderot University)

Abstract

We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. We provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. The proposed framework yields explicit valuation formulae for all linear interest rate derivatives as well as semi-closed formulae for non- linear derivatives via Fourier techniques and quantization. We show that a simple specification of the model can be successfully calibrated to market data.

Suggested Citation

  • Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2019. "Multiple Yield Curve Modelling with CBI Processes," Working Papers 19/2019, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:19/2019
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    References listed on IDEAS

    as
    1. Ernst Eberlein & Christoph Gerhart & Zorana Grbac, 2018. "Multiple curve L\'evy forward price model allowing for negative interest rates," Papers 1805.02605, arXiv.org.
    2. Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412.
    3. Anna Maria Gambaro & Ruggero Caldana & Gianluca Fusai, 2017. "Approximate pricing of swaptions in affine and quadratic models," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1325-1345, September.
    4. Damiano Brigo & Fabio Mercurio, 2001. "A deterministic-shift extension of analytically-tractable and time-homogeneous short-rate models," Finance and Stochastics, Springer, vol. 5(3), pages 369-387.
    5. Stéphane Crépey & Raphaël Douady, 2013. "Lois: credit and liquidity," Post-Print hal-01477998, HAL.
    6. 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.
    7. Giorgia Callegaro & Lucio Fiorin & Martino Grasselli, 2019. "Quantization meets Fourier: a new technology for pricing options," Annals of Operations Research, Springer, vol. 282(1), pages 59-86, November.
    8. Filipović, Damir & Trolle, Anders B., 2013. "The term structure of interbank risk," Journal of Financial Economics, Elsevier, vol. 109(3), pages 707-733.
    9. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    10. Pierre Collin‐Dufresne & Bruno Solnik, 2001. "On the Term Structure of Default Premia in the Swap and LIBOR Markets," Journal of Finance, American Finance Association, vol. 56(3), pages 1095-1115, June.
    11. Giorgia Callegaro & Andrea Mazzoran & Carlo Sgarra, 2019. "A Self-Exciting Modelling Framework for Forward Prices in Power Markets," Papers 1910.13286, arXiv.org.
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    Cited by:

    1. Frikha, Noufel & Li, Libo, 2021. "Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 76-107.
    2. Hainaut, Donatien, 2021. "Lévy interest rate models with a long memory," LIDAM Discussion Papers ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    More about this item

    Keywords

    Branching process; self-exciting process; multi-curve model; interest rate; Libor rate; OIS rate; multiplicative spread; affine process.;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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