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arXiv · 2509.25975

Rough SABR Forward Market Model

Reo Adachi·Masaaki Fukasawa·Naoki Iida·Mitsumasa Ikeda·Yo Nakatsu·Ryota Tsurumi·Tomohisa Yamakami
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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.

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Reo Adachi, Masaaki Fukasawa, Naoki Iida, Mitsumasa Ikeda, Yo Nakatsu, Ryota Tsurumi, Tomohisa Yamakami. 2025-09-30. Rough SABR Forward Market Model. https://arxiv.org/abs/2509.25975

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