Transfer-Entropy- and Hawkes-Process-Driven Dynamic Measurement of Cross-Border Financial Risk Contagion in Directed,...

Quantifying the direction, strength and temporal clustering of cross-border financial risk contagion calls for methods that go beyond linear correlation. We suggest a two-layer framework that brings together transfer entropy and a multivariate Hawkes self-exciting point process on a time-varying, directed, weighted network. In the first layer, one-to-one transfer entropies of sovereign credit default swap spreads are estimated with a bias-corrected k nearest neighbour estimator, and this step detects nonlinear and directional information transfer between spreads. The second layer is a multivariate Hawkes process that models how extreme loss events arrive and mutually excite one another across countries, and it gives an excitation intensity matrix, encoding the way a tail event in one country raises the likelihood of an instantaneous hazard occurring in another. By merging these two layers, we obtain a composite, directed, weighted adjacency matrix in which the weights of the edges reflect both information flow and event clustering. We introduce a network-level contagion intensity index and split it into direct, indirect and feedback terms using the graph Laplacian spectrum. Von Neumann graph entropy together with the spectral gap ratio serve as entropy-based measures of the complexity and fragility of the evolving network. We validate the choice of Shannon-type entropy through a Tsallis q-sensitivity analysis, and we verify the nonlinear dependence structure of the data using BDS tests and maximal Lyapunov exponent estimates. Three empirical findings emerge from analysing 20 sovereign CDS markets from January 2015 to December 2025: (i) directional risk spillover signals derived based on transfer entropy are more timely than those derived from variance decomposition; (ii) the Hawkes excitation component amplifies measured contagion intensity by 35 to 58 percent during the COVID-19 shock and the 2022 European energy crisis relative to a transfer-entropy-only baseline; (iii) von Neumann graph entropy reaches historically extreme values 7 to 12 trading days before the peak drawdown in a Global Sovereign Bond Index. These results hold across rolling window lengths, significance thresholds, alternative entropy functionals and alternative Hawkes kernels.