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Rough SABR Forward Market Model

Author

Listed:
  • Reo Adachi
  • Masaaki Fukasawa
  • Naoki Iida
  • Mitsumasa Ikeda
  • Yo Nakatsu
  • Ryota Tsurumi
  • Tomohisa Yamakami

Abstract

This paper advances interest rate modeling in the post-LIBOR era by introducing rough stochastic volatility into the Forward Market Model (FMM). We establish a rigorous asymptotic expansion of swaption implied volatility, connecting the FMM to a rough Bergomi-type framework for forward swap rates. This contribution bridges the gap between Heath-Jarrow-Morton (HJM)-consistent forward term rate models and forward swap rate models with stochastic volatility, offering a parsimonious yet precise framework for modeling swaption volatility surfaces. Furthermore, we justify and generalize the widely used "freezing" approximation within a rigorous mathematical framework. The proposed approach enhances the representation of persistent skew and term structure, addressing key challenges in modern fixed income markets.

Suggested Citation

  • Reo Adachi & Masaaki Fukasawa & Naoki Iida & Mitsumasa Ikeda & Yo Nakatsu & Ryota Tsurumi & Tomohisa Yamakami, 2025. "Rough SABR Forward Market Model," Papers 2509.25975, arXiv.org.
    • Handle: RePEc:arx:papers:2509.25975
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    References listed on IDEAS

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    1. Masaaki Fukasawa, 2022. "On asymptotically arbitrage-free approximations of the implied volatility," Papers 2201.02752, arXiv.org, revised Jan 2022.
    2. Masaaki Fukasawa, 2021. "Volatility has to be rough," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 1-8, January.
    3. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.
    4. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Hybrid scheme for Brownian semistationary processes," Finance and Stochastics, Springer, vol. 21(4), pages 931-965, October.
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