The weighted cross-shareholding complex network: a copula approach to concentration and control in financial markets

Abstract

In this work, we focus on the cross-shareholding structure in financial markets. Specifically, we build ad hoc indices of concentration and control by employing a complex network approach with a weighted adjacency matrix. To describe their left and right tail dependence properties, we explore the theoretical dependence structure between such indices through copula functions. The theoretical framework has been tested over a high-quality dataset based on the Italian Stock Market. In doing so, we clearly illustrate how the methodological setting works and derive financial insights. In particular, we advance calibration exercises on parametric copulas under the minimization of both Euclidean distance and entropy measure.

Vulnerability Analysis Method Based on Network and Copula Entropy

“…Unfortunately, despite the increasing sophistication of models and indicator methods, there are still problems, like the inability to dynamically demonstrate changes in market vulnerability and characterize market risk contagion. With the rapid development of complex network analysis methods and tools, these methods are increasingly used in financial research, such as equity structure research [ 10 , 11 ], risk contagion research [ 12 , 13 ], and so on. And, newer studies on financial vulnerability measures have also started to introduce weighted undirected graphs as abstract models of the financial system [ 14 , 15 , 16 , 17 , 18 , 19 ].…”