Systemic Risk Contagion in China’s Financial–Real Estate Network: Modeling and Forecasting via Fractional-Order PDEs

Modeling risk evolution in financial networks presents both practical and theoretical challenges, particularly during periods of heightened systemic stress. This issue has gained urgency recently in China as it faces unprecedented financial strain, largely driven by structural shifts in the real estate sector and broader economic vulnerabilities. In this study, we combine Fractional-order Partial Differential Equations (FoPDEs) with network-based analysis methods, proposing a hybrid framework for capturing and modeling systemic financial risk, which is quantified using the ΔCoVaR algorithm. The FoPDEs model is formulated based on reaction–diffusion equations and discretized using the Caputo fractional derivative. Parameter estimation is conducted through a composite optimization strategy, and numerical simulations are carried out to investigate the underlying mechanisms and dynamic behavior encoded in the equations. For empirical evaluation, we utilize data from China’s financial and real estate sectors. The results demonstrate that our model achieves a Mean Relative Accuracy (MRA) of 95.5% for daily-frequency data, outperforming LSTM and XGBoost under the same conditions. For weekly-frequency data, the model attains an MRA of 91.7%, exceeding XGBoost’s performance of 90.25%. Further analysis of parameter dynamics and event studies reveals that the fractional-order parameter α, which controls the memory effect of the model, tends to remain low when ΔCoVaR exhibits sudden surges. This suggests that the model assigns greater importance to past data during periods of financial shocks, capturing the persistence of risk dynamics more effectively.