Nonlinear Dynamics and Systemic Risk Measurement in Futures Markets Based on Entropy Theory and Multifractal Analysis

Futures markets exhibit nonlinear interactions, multi-scale dynamics, and non-stationary behaviour, rendering traditional linear risk models inadequate for tracing extreme-event transmission or measuring systemic fragility. We propose an integrated entropy–multifractal framework to measure systemic risk across three levels. At the micro level, High-Order Moment Multiscale Entropy quantifies local complexity. At the meso level, Weighted Cross Permutation Entropy and Multifractal Detrended Cross-Correlation Analysis identify directional contagion and tail co-movement. At the macro level, Multidimensional Scaling, Multivariate Permutation Entropy, and rolling-window analysis capture network structure, regime shifts, and time-varying risk.Using daily data from 16 global futures and financial variables (2018–2025), the empirical analysis yields three findings. Micro-level results show a structural divergence: emerging-market assets are extremely unpredictable, whereas developed-market assets maintain stable volatility. Meso-level findings reveal a stable causal hierarchy: energy markets transmit risk to agricultural commodities, while US–China equity co-movement is driven by common factors, not direct contagion. Macro-level results show that common factors dominate the futures system, with geopolitical risk isolated as exogenous; system complexity decays monotonically with horizon, and the complexity gradient signals crises in advance.We further propose and validate three risk indicators: the Fractal Vulnerability Index, the Causal Contagion Index, and the Systemic Chaos Indicator. These findings inform horizon-dependent portfolio construction, early-warning system design, and macro-prudential risk monitoring in futures markets.