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Dynamic Term Structure Models for SOFR Futures

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  • Jacob Bjerre Skov
  • David Skovmand

Abstract

The LIBOR rate is currently scheduled for discontinuation, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the $200 trillion market of derivatives and debt tied to the LIBOR. The only SOFR linked derivative with any significant liquidity and trading history is the SOFR futures contract, traded at the CME since 2018. We use the historical record of futures prices to construct dynamic arbitrage-free models for the SOFR term structure. The models allow you to construct forward-looking SOFR term rates, imply a SOFR discounting curve and price and risk and risk manage SOFR derivatives, not yet liquidly traded in the market. We find that a standard three-factor Gaussian arbitrage-free Nelson-Siegel model describes term rates very well but a shadow-rate extension is needed to describe the behaviour near the zero-boundary. We also find that the jumps and seasonal effects observed in SOFR, do not need to be specifically accounted for in a model for the futures prices. Finally we study the so-called convexity correction and find that it becomes significant beyond the 2 year maturity. For validation purposes we demonstrate that our model aligns closely with the methodology used by the Federal Reserve to publish indicative SOFR term rates.

Suggested Citation

  • Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic Term Structure Models for SOFR Futures," Papers 2103.11180, arXiv.org.
    • Handle: RePEc:arx:papers:2103.11180
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    File URL: http://arxiv.org/pdf/2103.11180
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    Cited by:

    1. David Skovmand & Jacob Bjerre Skov, 2022. "Decomposing LIBOR in Transition: Evidence from the Futures Markets," Papers 2201.06930, arXiv.org, revised Mar 2022.
    2. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    3. 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.
    4. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org, revised Nov 2024.
    5. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Working Papers hal-03898872, HAL.
    6. Fred Espen Benth & Nils Detering & Luca Galimberti, 2022. "Pricing options on flow forwards by neural networks in Hilbert space," Papers 2202.11606, arXiv.org.
    7. 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).
    8. Claudio Fontana, 2022. "Caplet pricing in affine models for alternative risk-free rates," Papers 2202.09116, arXiv.org, revised Jan 2023.
    9. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Papers 2202.00929, arXiv.org, revised Aug 2023.
    10. Fang, Dong-Jie & Yeh, Zong-Wei & He, Jie-Cao & Lin, Shih-Kuei, 2024. "What drives jumps in the secured Overnight Financing Rate? Evidence from the arbitrage-free Nelson–Siegel model with jump diffusion," Pacific-Basin Finance Journal, Elsevier, vol. 86(C).

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