The increasing interconnectedness and high dimensionality of modern financial markets have significantly increased the complexity of modelling systemic financial risk. Traditional econometric and volatility models often fail to capture nonlinear dependencies, structural instability, and noise contamination present in large financial datasets. This study proposes an advanced statistical modelling framework that combines spectral methods from Random Matrix Theory with data-driven dynamic modelling using Neural Stochastic Differential Equations to analyze systemic risk in high-dimensional financial systems.

Random Matrix Theory is applied to extract meaningful correlation structures from empirical covariance matrices of financial returns and to distinguish genuine market information from noise arising in large asset universes. This spectral filtering enables more stable estimation of correlation networks and improves the detection of systemic dependencies across financial institutions and assets. To capture the nonlinear stochastic evolution of market dynamics, neural stochastic differential equations are employed to learn drift and diffusion processes governing asset interactions and volatility propagation over time.

The integration of spectral statistical methods with neural stochastic modelling provides a flexible framework for identifying early warning signals of systemic instability and extreme financial events. Empirical experiments on high-dimensional financial datasets demonstrate that the proposed approach improves risk estimation and enhances the detection of emerging systemic vulnerabilities compared with conventional statistical models. By bridging tools from Applied Mathematics, Statistical Modelling, and Quantitative Finance, this research contributes to the development of robust analytical frameworks for systemic financial risk management.