Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Adachi, Reo, Fukasawa, Masaaki, Iida, Naoki, Ikeda, Mitsumasa, Nakatsu, Yo, Tsurumi, Ryota, Yamakami, Tomohisa
Institutions: The University of Osaka, The University of Tokyo
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7084091867
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