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Term structure modelling for multiple curves with stochastic discontinuities

Author

Listed:
  • Claudio Fontana

    (University of Padova)

  • Zorana Grbac

    (Université Paris Diderot)

  • Sandrine Gümbel

    (University of Freiburg)

  • Thorsten Schmidt

    (University of Freiburg
    Freiburg Institute of Advanced Studies (FRIAS)
    University of Strasbourg Institute for Advanced Study (USIAS))

Abstract

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and provide a fundamental theorem of asset pricing based on NAFLVR. The approach with stochastic discontinuities permits to embed market models directly, unifying seemingly different modelling philosophies. We also develop a tractable class of models, based on affine semimartingales, going beyond the requirement of stochastic continuity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:2:d:10.1007_s00780-020-00416-5
    DOI: 10.1007/s00780-020-00416-5
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Backwell, Alex & Hayes, Joshua, 2022. "Expected and Unexpected Jumps in the Overnight Rate: Consistent Management of the Libor Transition," Journal of Banking & Finance, Elsevier, vol. 145(C).
    2. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    3. Johannes Assefa & Philipp Harms, 2022. "Cylindrical stochastic integration and applications to financial term structure modeling," Papers 2208.03939, arXiv.org, revised May 2023.
    4. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Papers 2202.00929, arXiv.org, revised Aug 2023.
    5. Carassus, Laurence, 2023. "No free lunch for markets with multiple numéraires," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    6. 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.
    7. Harju, Antti J., 2024. "Target rate factors in short rate models," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    8. Claudio Fontana & Giacomo Lanaro & Agatha Murgoci, 2024. "The geometry of multi-curve interest rate models," Papers 2401.11619, arXiv.org, revised Jun 2024.
    9. Claudio Fontana & Eckhard Platen & Stefan Tappe, 2024. "Real-world models for multiple term structures: a unifying HJM framework," Papers 2411.01983, arXiv.org.
    10. Luca Galimberti & Anastasis Kratsios & Giulia Livieri, 2022. "Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis," Papers 2210.13300, arXiv.org, revised May 2023.
    11. Christa Cuchiero & Luca Di Persio & Francesco Guida & Sara Svaluto-Ferro, 2022. "Measure-valued processes for energy markets," Papers 2210.09331, arXiv.org.
    12. Laurence Carassus, 2021. "No free lunch for markets with multiple num\'eraires," Papers 2107.12885, arXiv.org, revised Dec 2022.
    13. Alan Brace & Karol Gellert & Erik Schlögl, 2024. "SOFR term structure dynamics—Discontinuous short rates and stochastic volatility forward rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(6), pages 936-985, June.

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    More about this item

    Keywords

    HJM model; Semimartingale; Affine process; NAFLVR; Large financial market;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • 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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