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Semi-analytical pricing of options written on SOFR futures

Author

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  • Andrey Itkin
  • Yerkin Kitapbayev

Abstract

In this paper, we propose a semi-analytical approach to pricing options on SOFR futures where the underlying SOFR follows a time-dependent CEV model. By definition, these options change their type at the beginning of the reference period: before this time, this is an American option written on a SOFR forward price as an underlying, and after this point, this is an arithmetic Asian option with an American style exercise written on the daily SOFR rates. We develop a new version of the GIT method and solve both problems semi-analytically, obtaining the option price, the exercise boundary, and the option Greeks. This work is intended to address the concern that the transfer from LIBOR to SOFR has resulted in a situation in which the options of the key money market (i.e., futures on the reference rate) are options without any pricing model available. Therefore, the trading in options on 3M SOFR futures currently ends before their reference quarter starts, to eliminate the final metamorphosis into exotic options.

Suggested Citation

  • Andrey Itkin & Yerkin Kitapbayev, 2024. "Semi-analytical pricing of options written on SOFR futures," Papers 2409.04903, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2409.04903
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    File URL: https://arxiv.org/pdf/2409.04903
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    References listed on IDEAS

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    1. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    2. Olivier Menoukeu-Pamen & Guangli Xu & Xiaoyang Zhuo, 2023. "Finite difference scheme versus piecewise binomial lattice for interest rates under the skew CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 23(5), pages 843-862, May.
    3. Kailin Ding & Zhenyu Cui & Xiaoguang Yang, 2023. "Pricing arithmetic Asian and Amerasian options: A diffusion operator integral expansion approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 217-241, February.
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    Cited by:

    1. Teemu Pennanen & Waleed Taoum, 2026. "Optimal Pricing and Hedging of SOFR Derivatives," Papers 2608.10711, arXiv.org.

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