Towards Generative Interest-Rate Modelling: Neural Perturbations Within the Libor Market Model

This study proposes a neural-augmented Libor Market Model (LMM) for swaption-surface calibration that enhances expressive power while maintaining the interpretability, arbitrage-free structure, and numerical stability of the classical framework. Classical LMM parametrizations, based on exponential-decay volatility functions and static correlation kernels, are known to perform poorly in sparsely quoted and long-tenor regions of swaption volatility cubes. Machine-learning–based diffusion models offer flexibility but often lack transparency, stability, and measure-consistent dynamics. To reconcile these requirements, the present approach embeds a compact neural network within the volatility and correlation layers of the LMM, constrained by structural diagnostics, low-rank correlation construction, and HJM-consistent drift. Empirical tests across major currencies (EUR, GBP, USD) and multiple quarterly datasets from 2024–2025 show that the neural-augmented LMM consistently outperforms the classical model. Improvements of approximately 9–15% in implied-volatility RMSE and 11–17% in PV RMSE are observed across all datasets, with no deterioration in any region of the surface. These results reflect the model’s ability to represent cross-tenor dependencies and surface curvature beyond the reach of classical parametrizations, while remaining economically interpretable and numerically tractable. The findings support hybrid model designs in quantitative finance, where small neural components complement robust analytical structures. The approach aligns with ongoing industry efforts to integrate machine learning into regulatory-compliant pricing models and provides a pathway for future generative LMM variants that retain arbitrage-free diffusion structure while learning data-driven volatility geometry.