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Caplet pricing in affine models for alternative risk-free rates

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  • Claudio Fontana

Abstract

Alternative risk-free rates (RFRs) play a central role in the reform of interest rate benchmarks. We study a model for RFRs driven by a general affine process. Under minimal assumptions, we derive explicit valuation formulas for forward-looking and backward-looking caplets/floorlets, term-basis caplets as well as 1-month and 3-month RFR futures contracts.

Suggested Citation

  • Claudio Fontana, 2022. "Caplet pricing in affine models for alternative risk-free rates," Papers 2202.09116, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2202.09116
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    References listed on IDEAS

    as
    1. Sander Willems, 2020. "SABR smiles for RFR caplets," Papers 2004.04501, arXiv.org, revised May 2020.
    2. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Papers 2202.00929, arXiv.org, revised Aug 2023.
    3. Berndt, Antje & Duffie, Darrell & Zhu, Yichao, 2020. "Across-the-Curve Credit Spread Indices," Research Papers 3884, Stanford University, Graduate School of Business.
    4. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    5. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    6. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic Term Structure Models for SOFR Futures," Papers 2103.11180, arXiv.org.
    7. Alessandro Gnoatto, 2012. "The Wishart Short Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-24.
    8. 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.
    9. Damiano Brigo & Fabio Mercurio, 2001. "A deterministic-shift extension of analytically-tractable and time-homogeneous short-rate models," Finance and Stochastics, Springer, vol. 5(3), pages 369-387.
    10. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2017. "Geometric Asian option pricing in general affine stochastic volatility models with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 873-888, June.
    11. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2019. "Affine multiple yield curve models," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 568-611, April.
    12. Andrea Macrina & David Skovmand, 2020. "Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks," Risks, MDPI, vol. 8(1), pages 1-18, March.
    13. Marc Henrard, 2004. "Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model," Finance 0402008, University Library of Munich, Germany.
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