Multi-Scale Modeling of Financial Systems Using Neural Differential Equations: Applications to High-Frequency Trading, Regime Switching, and Portfolio Optimization

This paper explores the application of neural differential equations (NDEs) to model the multi-scale dynamics of financial systems, with a focus on high-frequency trading, regime-switching asset prices, and portfolio optimization. We propose a novel framework that integrates stochastic volatility and hierarchical architectures to capture both short-term fluctuations and long-term trends. e demonstrate the effectiveness of NDEs in predicting prices, identifying regime transitions, and optimizing portfolios across multiple time scales. The framework is compared with traditional methods such as GARCH and LSTMs, showing superior performance in terms of predictive accuracy, computational efficiency, and risk-adjusted returns. The results highlight the potential of NDEs for real-time applications in financial markets, offering a scalable and interpretable solution for modeling complex systems.