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Term structure modelling with overnight rates beyond stochastic continuity

Author

Listed:
  • Claudio Fontana
  • Zorana Grbac

    (UPCité - Université Paris Cité)

  • Thorsten Schmidt

Abstract

In the current reform of interest rate benchmarks, a central role is played by risk-free rates (RFRs), such as SOFR (secured overnight financing rate) in the US. A key feature of RFRs is the presence of jumps and spikes at periodic time intervals as a result of regulatory and liquidity constraints. This corresponds to stochastic discontinuities (i.e., jumps occurring at predetermined dates) in the dynamics of RFRs. In this work, we propose a general modeling framework where RFRs and term rates can have stochastic discontinuities and characterize absence of arbitrage in an extended HJM setup. When the term rate is generated by the RFR itself, we show that it solves a BSDE, whose driver is determined by the HJM drift restrictions. In general, this BSDE may admit multiple solutions and we provide sufficient conditions ensuring uniqueness. We develop a tractable specification driven by affine semimartingales, also extending the classical short rate approach to the case of stochastic discontinuities. In this context, we show that a simple specification allows to capture stylized facts of the jump behavior of overnight rates. In a Gaussian setting, we provide explicit valuation formulas for bonds and caplets. Finally, we study hedging in the sense of local risk-minimization when the underlying term structures have stochastic discontinuities.

Suggested Citation

  • Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Working Papers hal-03898872, HAL.
    • Handle: RePEc:hal:wpaper:hal-03898872
    Note: View the original document on HAL open archive server: https://hal.science/hal-03898872v1
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    References listed on IDEAS

    as
    1. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic Term Structure Models for SOFR Futures," Papers 2103.11180, arXiv.org.
    2. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    3. Claudio Fontana & Markus Pelger & Eckhard Platen, 2017. "On the existence of sure profits via flash strategies," Papers 1708.03099, arXiv.org, revised Jul 2019.
    Full references (including those not matched with items on IDEAS)

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