SDE-Constrained Lévy-Driven Neural SDEs for Predictability-Aware Exchange Rate Forecasting

Exchange-rate forecasting requires modelling non-stationary dynamics, heavy-tailed shocks, and complex temporal dependencies. However, forecasting performance in emerging-market currencies is fundamentally constrained by intrinsic dynamical instability, while most existing approaches are evaluated primarily through predictive accuracy rather than the predictability limits of the underlying system. This paper develops a predictability-aware framework that combines nonlinear dynamical diagnostics with a Lévy-driven neural stochastic differential equation model. Drift and diffusion are parameterized by neural networks and driven by α-stable Lévy motion, enabling the representation of non-Gaussian fluctuations, abrupt shocks, and regime changes. To learn under discontinuous dynamics, we introduce a structurally constrained training objective based on a strong-form discretization of the underlying SDE. To characterise intrinsic predictability, we employ phase-space reconstruction and maximal Lyapunov exponent estimation. These diagnostics are interpreted as finite-sample measures of trajectory divergence and effective instability in a stochastic system, rather than evidence of low-dimensional deterministic chaos—a distinction motivated by well-documented limitations of chaos testing in financial data. Experiments on multiple West African currency pairs demonstrate competitive short-horizon forecasting performance relative to econometric and neural baselines while providing a principled framework for analysing predictability degradation under heavy-tailed stochastic dynamics. Across currencies and model classes, forecasting accuracy deteriorates beyond horizons comparable to the estimated Lyapunov time, suggesting that forecast degradation reflects intrinsic dynamical instability rather than model-specific limitations. The results support the view that reliable exchange-rate prediction is fundamentally a short-horizon problem and illustrate how stochastic dynamical modelling and predictability diagnostics can be combined to characterise forecasting limits in heavy-tailed financial systems.