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Term structure modelling with overnight rates beyond stochastic continuity

Author

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  • Claudio Fontana
  • Zorana Grbac
  • Thorsten Schmidt

Abstract

Overnight rates, such as the SOFR (Secured Overnight Financing Rate) in the US, are central to the current reform of interest rate benchmarks. A striking feature of overnight rates is the presence of jumps and spikes occurring at predetermined dates due to monetary policy interventions and liquidity constraints. This corresponds to stochastic discontinuities (i.e., discontinuities occurring at ex-ante known points in time) in their dynamics. In this work, we propose a term structure modelling framework based on overnight rates and characterize absence of arbitrage in a generalised Heath-Jarrow-Morton (HJM) setting. We extend the classical short-rate approach to accommodate stochastic discontinuities, developing a tractable setup driven by affine semimartingales. In this context, we show that simple specifications allow to capture stylized facts of the jump behavior of overnight rates. In a Gaussian setting, we provide explicit valuation formulas for bonds and caplets. Furthermore, we investigate hedging in the sense of local risk-minimization when the underlying term structures feature stochastic discontinuities.

Suggested Citation

  • Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Papers 2202.00929, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2202.00929
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    File URL: http://arxiv.org/pdf/2202.00929
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    References listed on IDEAS

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    1. Sander Willems, 2020. "SABR smiles for RFR caplets," Papers 2004.04501, arXiv.org, revised May 2020.
    2. 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.
    3. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    4. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic Term Structure Models for SOFR Futures," Papers 2103.11180, arXiv.org.
    5. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic term structure models for SOFR futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1520-1544, October.
    6. Karol Gellert & Erik Schlogl, 2021. "Short Rate Dynamics: A Fed Funds and SOFR perspective," Papers 2101.04308, arXiv.org.
    7. Marc Pierre Henrard, 2019. "LIBOR Fallback and Quantitative Finance," Risks, MDPI, vol. 7(3), pages 1-15, August.
    8. Claudio Fontana & Markus Pelger & Eckhard Platen, 2017. "On the existence of sure profits via flash strategies," Papers 1708.03099, arXiv.org, revised Jul 2019.
    9. Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    10. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    11. Frank Gehmlich & Thorsten Schmidt, 2018. "Dynamic Defaultable Term Structure Modeling Beyond The Intensity Paradigm," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 211-239, January.
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    Cited by:

    1. Claudio Fontana, 2022. "Caplet pricing in affine models for alternative risk-free rates," Papers 2202.09116, arXiv.org, revised Jan 2023.

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