Systemic Risk and Complex Systems: A Graph-Theory Analysis

This chapter summarizes several empirical studies in finance, undertaken through the prism of the graph theory. In these studies, we built graphs in order to investigate integration and systemic risk in derivative markets. Several classes of underlying assets (i.e. energy products, metals, financial assets, agricultural products) are considered, on a twelve-year period. In such a high dimensional analysis, the graph theory enables us to understand the dynamic behavior of our price system. The dimension of the fully connected graph being high, we rely on a specific type of graphs: Minimum Spanning Trees (MSTs). Such a tree is especially interesting for the study of systemic risk: it can be assimilated into the shortest and most probable path for the propagation of a price shock. We first examine the topology of the MSTs. Then, given the time dependency of our correlation-based graphs, we study their evolution over time and their stability.