Rough SABR Forward Market Model

Paper: arXiv 2509.25975

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical contribution by integrating rough volatility into the post-LIBOR Forward Market Model and rigorously formalizing the freezing approximation using advanced stochastic calculus and asymptotic expansions. However, empirical rigor is limited primarily to illustrative calibration experiments without extensive out-of-sample backtesting, and code is not explicitly provided.

Research Flowchart

  flowchart TD
    A[Research Goal: Advance Interest Rate Modeling in Post-LIBOR Era] --> B[Input: Rough Stochastic Volatility & Forward Market Model]
    B --> C[Method: Apply & Mathematically Justify Freezing Approximation]
    C --> D[Computation: Derive Asymptotic Expansion for Swaption Implied Volatility]
    D --> E[Outcome: Connect FMM to Rough Bergomi-type Framework]
    E --> F[Outcome: Precise Modeling of Persistent Skew & Term Structure]

Cited References (12)

1. Hybrid scheme for Brownian semistationary processes (2017)
2. The microstructural foundations of leverage effect and rough volatility (2018)
3. Parametrising correlation matrices (2020)
4. Volatility has to be rough (2021)
5. A rough SABR formula (2022)
6. On asymptotically arbitrage-free approximations of the implied volatility (2022)
7. Hedging under rough volatility (2023)
8. On swap rate dynamics: To freeze or not to freeze? (2017)

0 of 12 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.