The study addresses the critical issue of risk control in the complex system of the industrial chain, focusing on the mining stock market in China. The research is motivated by the “carbon neutrality” goal and the resulting uncertainty and volatility in the mining financial market. Existing research on price volatility primarily uses time-series analysis methods like Pearson correlation, Granger causality, and pattern causality. While copula models, DCC models, and GARCH models have been used to study volatility spillover, the authors aim to incorporate network structure control theory for a more comprehensive approach to risk management. Previous risk control studies have focused on macroeconomic indicators, corporate financial information, and capital market information, often employing machine learning models. However, this research introduces a novel framework combining econometrics, cascade conduction, and structural control theories to manage price fluctuation risks within the industrial chain.

The literature review highlights the existing research on price fluctuation, focusing on time-series analysis methods like Pearson correlation, Granger causality, and pattern causality. The authors note that copula models, DCC models, and GARCH models are used increasingly to study volatility spillover. Previous risk control studies have focused on macroeconomic indicators, corporate financial information, and capital market information, often using machine learning models. The authors discuss the limitations of existing approaches, particularly the lack of integration of network structure control theory into financial risk management. The concept of network controllability, originally proposed by Lombardi and Hrnquist (2007), and its subsequent development by Liu et al. (2011) and others, is presented as a foundation for this study.

The study employs a multi-stage methodology. First, a BEKK-GARCH model is used to measure volatility spillover effects between stocks, considering both shock and volatility effects. Second, a DCC-GARCH model is used to calculate systematic spillover risk (Delta CoVaR) and construct a risk cascade conduction network model based on CoVaR. A sliding window method (240-day window, 5-day step) is used to create a dynamic network. The industrial driving coefficient, calculated using the backward correlation from an input-output table, and an anti-risk ability index (based on the Z-value) are incorporated to adjust the risk spillover values. Third, a risk control network model is built using network control dynamics and minimum energy consumption theories. The Kalman condition is used to assess system controllability, and the control input is calculated to minimize energy consumption. Finally, different scenarios (whole-industry chain, upper-middle layer, upper-lower layer, middle-lower layer networks) are analyzed to determine risk regulation signals and control strategies, considering the initial state VaR and the target state (0.9*VaR).

The study identifies key risk conduction nodes within the mining stock market, considering conduction range, strength, and number. Results show a positive correlation between these three dimensions, indicating that stronger and longer-lasting risk conduction involves a greater number of nodes. A small percentage of nodes (less than 20%) significantly affect risk conduction, aligning with the Pareto principle. Analysis across different network scenarios (whole-industry chain, upper-middle, upper-lower, middle-lower) reveals that metal smelting stocks in the middle layer play a critical role in risk conduction across various scenarios, with some specific stocks repeatedly identified as key risk nodes. Dynamic simulation of risk control in two-layer and three-layer networks demonstrates that the upper-lower layer network is easier to control than other configurations. The cost of risk control, including regulation cost, time cost, and node number cost, is significantly higher for the three-layer (whole-industry chain) network compared to two-layer networks. The study recommends focusing on key risk stocks identified in different scenarios and utilizing appropriate monetary policies (loosening monetary policy to inject capital and stabilize the market) to mitigate risk.

The findings highlight the significant impact of industry-driving effects on risk conduction within the mining stock market, underscoring the need for risk management from an industrial chain perspective. The study confirms the effectiveness of network control dynamics in identifying key risk nodes and devising control strategies. The substantial differences in risk control costs between two-layer and three-layer networks emphasize the increased complexity and difficulty of managing risks in more interconnected systems. The recommendation of loose monetary policies aligns with previous instances of market interventions in China, suggesting the practical applicability of the proposed approach. The study’s focus on specific key stocks and their industrial positions offers actionable insights for market regulators and policymakers.

This paper makes significant contributions by integrating network control dynamics and industrial chain theory into risk control of mining stocks. It identifies key risk nodes and proposes targeted control strategies for different network structures. The study highlights the importance of considering industry driving effects and network complexity in risk management. Future research could explore incorporating risk supervision concepts and policies from the actual mining financial market into the model for more nuanced and effective risk control.

The model primarily focuses on network dynamics and structural control theory, without fully incorporating real-world risk supervision concepts and policies. The study uses data from a specific period (2020-2021), and the generalizability of findings to other time periods or markets needs further investigation. The simplification of the industrial chain into layers may not fully capture the intricate relationships within the mining industry.