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Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks

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  • Andrea Macrina

    (Department of Mathematics, University College London, London WC1E 6BT, UK
    African Institute for Financial Markets and Risk Management, University of Cape Town, Rondebosch 7701, South Africa)

  • David Skovmand

    (Department of Mathematics, University of Copenhagen, 2100 Copenhagen, Denmark)

Abstract

Interest rate benchmarks are currently undergoing a major transition. The LIBOR benchmark is planned to be discontinued by the end of 2021 and superseded by what ISDA calls an adjusted risk-free rate (RFR). ISDA has recently announced that the LIBOR replacement will most likely be constructed from a compounded running average of RFR overnight rates over a period matching the LIBOR tenor. This new backward-looking benchmark is markedly different when compared with LIBOR. It is measurable only at the end of the term in contrast to the forward-looking LIBOR, which is measurable at the start of the term. The RFR provides a simplification because the cash flows and the discount factors may be derived from the same discounting curve, thus avoiding—on a superficial level—any multi-curve complications. We develop a new class of savings account models and derive a novel interest rate system specifically designed to facilitate a high degree of tractability for the pricing of RFR-based fixed-income instruments. The rational form of the savings account models under the risk-neutral measure enables the pricing in closed form of caplets, swaptions and futures written on the backward-looking interest rate benchmark.

Suggested Citation

  • Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:1:p:23-:d:327778
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    References listed on IDEAS

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    1. Alfeus, Mesias & Grasselli, Martino & Schlögl, Erik, 2020. "A consistent stochastic model of the term structure of interest rates for multiple tenors," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    2. Marc Pierre Henrard, 2019. "LIBOR Fallback and Quantitative Finance," Risks, MDPI, vol. 7(3), pages 1-15, August.
    3. Jirô Akahori & Andrea Macrina, 2012. "Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 1, pages 1-15, World Scientific Publishing Co. Pte. Ltd..
    4. Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Papers 0910.5033, arXiv.org.
    5. Marek Rutkowski, 1997. "A note on the Flesaker-Hughston model of the term structure of interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 151-163.
    6. Andrea Macrina, 2014. "Heat Kernel Models For Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-34.
    7. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    9. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    10. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    11. Jacob Gyntelberg & Philip Wooldridge, 2008. "Interbank rate fixings during the recent turmoil," BIS Quarterly Review, Bank for International Settlements, March.
    12. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
    13. Stéphane Crépey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2016. "Rational multi-curve models with counterparty-risk valuation adjustments," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 847-866, June.
    14. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
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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.
    2. 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.
    3. Sander Willems, 2020. "SABR smiles for RFR caplets," Papers 2004.04501, arXiv.org, revised May 2020.
    4. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org.
    5. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Papers 2202.00929, arXiv.org, revised Aug 2023.

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