Extreme risk spillovers in international energy markets: New insights from multilayer networks in the frequency domain

This paper constructs multilayer risk spillover networks in the frequency domain, containing short-, medium-, and long-term layers, to explore extreme risk spillovers in international energy markets at different frequency bands. We analyze the topology properties of multilayer networks at the system, region, and country levels. Based on daily data from 20 national energy stock markets spanning 2006–2023, the empirical results show that: (1) The overall topology of multilayer networks, including the edge structure and spillover strength structure, exhibit frequency heterogeneity. With the onset of a major crisis, the frequency heterogeneity of the network topology increases significantly, and international energy risk spillovers tend to concentrate in fewer layers (i.e., over one or two frequency bands). (2) Long-term risk is primarily responsible for the extreme risk spillover behavior between energy markets. (3) Compared to short- and medium-term spillovers, long-term spillovers are more crisis-sensitive. Furthermore, long-term spillovers within different regions vary in their sensitivity to local or global crises. (4) As market conditions fluctuate, the key players driving the short-term layer change, whereas those driving the medium- and long-term layers remain relatively stable. Overall, our findings provide new insights for policymakers and investors to prevent international energy systemic risks and optimize investment strategies.