Exploring crypto-stock risk contagion via directed complex network analytics

In the context of financial market integration and convergence of investor behavior, the risk contagion between cryptocurrency and traditional financial markets has become increasingly significant. We construct a risk spillover matrix using the Elastic-Net-GFEVD（Generalized Forecast Error Variance Decomposition）method, encompassing major global stock indices and cryptocurrencies. Based on this matrix, we develop a cryptocurrency risk contagion network employing DMST(Directed Minimum Spanning Tree) and DPMFG(Directed Planar Maximally Filtered Graph) techniques. The INFOMAP algorithm is further applied to identify network communities, enabling the tracking of risk spillover effects across time and regions. To capture the dynamic evolution of risk spillovers and network connectivity, we utilize TVP-VAR(Time-Varying Parameter Vector Autoregressive Model) and smoothing techniques. Our findings indicate that U.S. and European markets exhibit the highest risk spillovers to cryptocurrencies among all regions, and Ethereum is the cryptocurrency with the greatest risk spillover. The COVID-19 pandemic has reshaped the dynamics of risk transmission between stock and cryptocurrency markets. Before the pandemic, stock markets were tightly interconnected, while the cryptocurrency market operated largely independently. Post-pandemic, economic uncertainty has intensified risk spillovers, especially from U.S. and European stock markets to cryptocurrencies. LTC was the most impacted index in the latter half of 2021, while Ethereum was most affected by spillovers in mid-2021 and exhibited the highest contagion by the end of 2022. This shift—from risk recipient to active transmitter—underscores the increasing systemic importance of select cryptocurrency indices in the global financial network. This research offers key insights for regulators to mitigate systemic risk contagion between cryptocurrencies and global stock markets.