Rough SABR Forward Market Model
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.
Keywords
Cite
@article{arxiv.2509.25975,
title = {Rough SABR Forward Market Model},
author = {Reo Adachi and Masaaki Fukasawa and Naoki Iida and Mitsumasa Ikeda and Yo Nakatsu and Ryota Tsurumi and Tomohisa Yamakami},
journal= {arXiv preprint arXiv:2509.25975},
year = {2025}
}
Comments
40 pages