This document analyzes banking networks from 2000 to 2018 using network analysis methods. It defines banking networks with countries as nodes and cross-border banking exposures as weighted, directed edges. Three network types are examined: full, core-periphery, and core-core. Topological indicators like degree, strength, and clustering coefficients are calculated for each country and network averages over time. Graphs show the evolution of network structure from 2000 to 2008 to 2018. Insights into country rankings and indicator trends provide information on systemic risk in the global banking network.

1. Network Analysis to
assess systemic risk
Supervisor: Chiara Pederzoli
Graduand: Mirko Prazzoli
Matr. N. 777310
Academic Year: 2018/2019

2. Systemic Risk: An introduction
• «systemic risk is any set of circumstances that threatens the
stability of or public confidence in the financial system» (cit
Billio et al, 2010).
• Recent literature (Minoiu&Reyes 2013 and Bongini et al
2018) has focused on the study of systemic risk with the
application of the Network Analysis.

3. Network definition
• A network is, in its simplest form, a collection of points joined together
in pairs by lines.
• In the jargon of the field the points are referred to as vertices or nodes
and the lines are referred to as edges.

4. Networks topologies and their mathematical representation
Consider a simple network with m (binary) edges and n vertices labeled with integers 1,2,
... , n to refer to any vertex unambiguously; then its “adjacency matrix” is a matrix A of nxn
dimension with elements aij:
Whereas, in the case of a directed network, the elements aij are given by:
Finally, in the case of a weighted network, we have an extension of the previous versions
and an “adjacency matrix” W with link weights (wij).

5. Purpose and definition of the analyzed networks
• The purpose of the current work is to analyze the structural properties of the
global banking network (GBN) in the period between fourth quarter 2000 and
third quarter 2018, with data provided by the Bank for International Settlements
(BIS) for 220 countries.
• In the current analysis, each country in the chosen dataset represents a vertex of
the network and weighted directed edges among vertices indicate positive cross-
border exposures (CBS and IB) of a country banking system to other countries.
• For instance, an edge from country X to country Y represents the aggregate
investment exposure of country X’s banking system in country Y.
• Each quarter observation of our sample period has been modeled as a separate
network, and the analysis is focused on three different type of network.

6. Three types of network
• The full network: which refers to all available
data.
• The core-periphery network: based on edges
between the core and the periphery.
• The core-core network: which is limited to the 16
countries that make up the core.
Our sample contains 220 countries, of which 16
are advanced economies (about 97.32 percent of
total bank-intermediated flows of all BIS reporting
countries) that report bilateral positions to the BIS
(reporting countries) and 204 are countries vis-à-
vis which positions are reported (non-reporting
countries).

7. Topological indicators used in the analysis
• Degree: the number of edges connected to a vertex i is called degree of a
vertex in its network.
• Strength: the degree of a vertex weighted for the importance of the
edges.
• In Clustering Coefficient: as the ratio between the number of triangles of
that pattern actually formed by v and the total number of triangles of that
pattern that v can possibly form.

8. Empirical results

9. Country rankings: top player in the GBN out degree and strength

10. Country rankings: binary in-Clustering Coefficient

11. Country rankings: weighted in-Clustering Coefficient

12. Average in-Clustering Coefficients of the full and core-periphery networks

13. Graphs of the core-periphery network
2000-Q4 2008-Q1
2018-Q3

14. Graphs of the full network
2000-Q4 2008-Q1
2018-Q3

15. Graphs of the core-core network
2000-Q4 2008-Q1
2018-Q3

16. INDICATOR INSIGHTS

17. Average out-indicators of the full network

18. Average out-indicators of the core-periphery network