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Term structure modelling for multiple curves with stochastic discontinuities

Author

Listed:
  • Claudio Fontana
  • Zorana Grbac

    (UPCité - Université Paris Cité)

  • Sandrine Gümbel
  • Thorsten Schmidt

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 modeling 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," Post-Print hal-03898927, HAL.
    • Handle: RePEc:hal:journl:hal-03898927
    DOI: 10.1007/s00780-020-00416-5
    Note: View the original document on HAL open archive server: https://hal.science/hal-03898927v1
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    References listed on IDEAS

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    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. Cuchiero, Christa & Di Persio, Luca & Guida, Francesco & Svaluto-Ferro, Sara, 2024. "Measure-valued affine and polynomial diffusions," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    3. Carassus, Laurence, 2023. "No free lunch for markets with multiple numéraires," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    4. 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.
    5. Harju, Antti J., 2024. "Target rate factors in short rate models," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    6. Claudio Fontana & Giacomo Lanaro & Agatha Murgoci, 2024. "The geometry of multi-curve interest rate models," Papers 2401.11619, arXiv.org, revised Jun 2024.
    7. Claudio Fontana & Eckhard Platen & Stefan Tappe, 2024. "Real-world models for multiple term structures: a unifying HJM framework," Papers 2411.01983, arXiv.org.

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