Rough SABR Forward Market Model
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908568609882112 |
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| author | Adachi, Reo Fukasawa, Masaaki Iida, Naoki Ikeda, Mitsumasa Nakatsu, Yo Tsurumi, Ryota Yamakami, Tomohisa |
| author_facet | Adachi, Reo Fukasawa, Masaaki Iida, Naoki Ikeda, Mitsumasa Nakatsu, Yo Tsurumi, Ryota Yamakami, Tomohisa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rough SABR Forward Market Model Adachi, Reo Fukasawa, Masaaki Iida, Naoki Ikeda, Mitsumasa Nakatsu, Yo Tsurumi, Ryota Yamakami, Tomohisa Mathematical Finance 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. |
| title | Rough SABR Forward Market Model |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2509.25975 |