A Novel Framework for Outlier Detection in Financial Markets: A Complex Network Approach with Visibility Graphs

Li Hao¹Linan Chen²Gaixian Chai^3*Luyi Zhang⁴

• ¹Henan University of Economic and Law, Zhengzhou, China
• ²Yunnan University of Finance and Economics, Kunming, China
• ³Hubei Business College, Wuhan, China
• ⁴Inner Mongolia University, Hohhot, China

The increasing complexity and nonlinearity of financial markets render traditional linear models inadequate for systemic risk assessment. This paper proposes a novel framework for identifying outlier events and critical transitions in financial markets by integrating a Complex Network Approach with Visibility Graph Algorithms. We first construct a comprehensive Financial Stress Index (FSI) for China by aggregating tailored sub-indices from the bond, stock, money, and foreign exchange markets, incorporating time-varying cross-market correlations. The time series of the resulting FSI and sub-indices are then mapped into complex networks using a visibility graph algorithm. To identify critical risk nodes within these networks, we introduce a Rayleigh Entropy-Based Overlapping Influence Algorithm, which accounts for node inter-dependencies and network loops often neglected by conventional percolation theories. Applied to daily data from January 2015 to June 2025, our method not only effectively pinpoints key stress periods but also reveals cross-market stress transmission paths via a Vector Autoregression (VAR) model, a stock market shock leads to a 0.08 increase in the bond market stress index within 5 trading days. We further quantify policy impacts: for instance, a reserve requirement ratio cut by the PBOC reduces the money market stress index by an average of 0.12 within 30 days. The results show that stress originates from and propagates across different sub-markets with measurable time lags, with bond market credit spreads being the dominant driver of FSI stochastic fluctuations. This network-based approach, combined with model-driven transmission analysis, offers a powerful, dynamic tool for enhancing the monitoring and early warning of financial systemic risk, providing data-backed insights for both researchers and policymakers.