Interbank Network Analysis
Key Question:
If one bank were to face an adverse shock, how
would the rest of the banking / financial system be
affected?
Potential Solution:
Analysis using network modelling tools
2
Outline

Introduction

Why network models?

Approaches to network analysis

Constructing a network graph
3
Introduction

ULTIMATE GOAL: A model to examine the role of
financial contagion in the banking system, which also
seeks to obtain the aggregate losses for the financial
system.

Using network theory, we study the structure of the
banking system which is composed of banks that
are connected by their interbank bilateral
exposures.
4
Introduction

Where are network models used?

Intelligence agencies identify criminal and terrorist
networks from traces of communication that they
collect; and then identify key players in these networks.

Social networking websites like Facebook identify and
recommend potential friends based on friends-offriends.

Epidemiologists track spread of diseases.

Central banks for mapping interlinkages between FIs.
5
Introduction

Among central banks, who is using them?


Most central banks favour network analysis because


Bank of England , Deutsche Bundesbank, European Central Bank,
Reserve Bank of India, South African Reserve Bank etc.
Visual understanding

Uncover patterns in relationships or interactions which may not be readily
clear in the numbers.

Follow the paths that information (liquidity, panic) follows in financial
systems.
Once data is mapped as a network, it is easy to simulate the
propagation of systemic shocks and crises due to contagion.
6
Why network models?

Interconnectedness within the banking system proved to
be a key driver of systemic risk in the 2008 global financial
crisis.

The crisis emphasised how network linkages and
interactions between banks are critical to understanding
systemic risk.

It is important for financial stability analysts to have a
sound understanding of the level of and changes in
financial interconnectedness.
7
Why network models?

Viewing the banking system as a network is useful in analysing the
effects that the failure of a bank may produce.

It is important to understand how the risk of systemic breakdown
relates to the type and number of institutions that comprise the
banking system.

Furthermore, a study of the concentration of the banking system helps
us to focus on:

the role of direct interbank connections as a source of systemic risk,

the potential for knock-on defaults that are created by such exposures,

how adequately capital regulation would address the risk of systemic
breakdown that arises in the banking sector.
8
Why network models?
Causes of simultaneous bank
failure, Nier (2008)
feedback effects
from endogenous
fire-sale of assets by
distressed
institutions
direct bilateral
exposures
between
banks
simultaneous
failure of
banks
correlated
exposures of
banks to a
common source
of risk
informational
contagion
9
Approaches to network analysis

Allen and Gale (2000)

Examine the different types of networks by completeness and
interconnected.

The connections created within interbank system can guard against
liquidity shocks, although these same interlinkages may act as
catalyst for multiple bank failures in the event of default by a single
institution.

In addition to investigating the response of different network
structures to the risk of contagion, they conclude that complete
claims structures are shown to be more robust than incomplete
structures.
10
Approaches to network analysis
Types of networks, Allen and Gale (2000)
Complete market
Incomplete market
structure
structure
Disconnected
incomplete market
structure
11
Approaches to network analysis

Sachs (2010)

Makes assumptions such as maximum entropy regarding the
structure of interbank exposures .

Finds that the stability of a financial system depends not only on
the completeness and interconnectedness of the network, but also
on the distribution of interbank exposures within the network.

A network with money centres with asset concentration among
core banks is likely to be more unstable than systems with banks of
homogeneous size in a random network.

A money centre is a network system where few large banks are strongly
interconnected and a large number of small banks in the periphery are
only connected to one core bank but not to other banks in the network.
12
Approaches to network analysis
A money centre model with 3 core banks, Sachs (2008)
13
Approaches to network analysis

Minou and Reyes (2012):

Analyse the global banking network for 184 countries during 1978-2010.

Density of the global banking network defined by cross-border banking flows is pro-cyclical,
expanding and contracting with the global cycle of capital flows.

Connectedness in the network tends to rise before banking and debt crises and fall in the
aftermath.

Iori et al (2008), Nier et al (2008) and Li et al (2010) apply the theory of complex
networks in describing the interbank market.

Bank of Uganda:

Define the credit lending relationships of banks in the Ugandan interbank market using network
theory, enabling the study of various degrees of connectivity in the network over time in a
systematic way.

Examine how small changes in the underlying parameters can have a significant impact on the
stability of networks.
14
Constructing a network graph

Type of data for interbank network analysis varies;

Direct interbank market bilateral exposures

For different types of markets and transactions e.g. secured and
unsecured lending, FX exposures, swaps, securities

Data from payments systems

Vary by size of transactions

Analysis can be performed for varied frequencies e.g. daily,
weekly or monthly.

Data is arranged in an adjacency matrix to reflect bilateral
exposures.
15
Constructing a network graph

Each bank is represented by a node on the network,
and the bilateral interbank exposures of each bank
define the links with other banks.

These links may be directed or undirected


Directed network: interbank connections comprise both
assets and liabilities; no netting of exposures is
assumed.

Undirected network
Also, network may be weighted or unweighted.
16
Constructing a network graph
Unweighted networks
A
I
B
F
J
C
E
K
D
L
M
N
G
H
A
0
0
0
1
0
0
0
0
0
0
0
1
0
1
I
1
0
0
0
0
0
0
0
0
0
0
0
0
0
B
0
0
0
0
0
0
0
0
0
0
0
0
0
0
F
0
0
1
0
0
0
0
0
1
0
0
1
0
0
J
0
0
1
0
0
0
0
0
0
0
0
1
0
0
C
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E
0
0
0
0
0
1
0
0
1
0
0
1
0
0
K
0
0
0
0
0
1
0
0
1
0
0
1
0
0
D
0
0
0
0
0
0
0
0
0
0
0
0
0
0
L
0
0
0
0
0
0
0
0
1
0
0
0
0
0
M
0
0
0
0
0
0
0
0
1
0
0
1
0
0
N
0
0
0
1
0
0
1
0
0
0
0
0
1
0
G
0
0
0
0
0
0
0
0
0
0
0
0
0
0
H
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17
Constructing a network graph
Unweighted networks
18
Constructing a network graph
Weighted networks
A
I
B
F
J
C
E
K
D
L
M
N
G
H
A
0
0
0
17.6
0
0
0
0
0
0
0
2
0
1
I
1
0
0
0
0
0
0
0
0
0
0
0
0
0
B
0
0
0
0
0
0
0
0
0
0
0
0
0
0
F
0
0
2.7
0
0
0
0
0
5
0
0
13
0
0
J
0
0
6.5
0
0
0
0
0
0
0
0
9
0
0
C
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E
0
0
0
0
0
8.4
0
0
15
0
0
9.5
0
0
K
0
0
0
0
0
20
0
0
30
0
0
3.5
0
0
D
0
0
0
0
0
0
0
0
0
0
0
0
0
0
L
0
0
0
0
0
0
0
0
1
0
0
0
0
0
M
0
0
0
0
0
0
0
0
25
0
0
12.5
0
0
N
0
0
0
48.4
0
0
40
0
0
0
0
0
60
0
G
0
0
0
0
0
0
0
0
0
0
0
0
0
0
H
0
0
0
0
0
0
0
0
0
0
0
0
0
0
19
Constructing a network graph
Weighted networks
20
Properties of the interbank network

In order to gain a deeper understanding of the dynamic’s of the
interbank system, we consider a range of commonly used indicators of
cohesion, centrality and distribution as aggregate network measures.

These indicators are used to investigate the statistical and structural
properties of the interbank system.

Centrality measures enable us to study the distribution of banks within
the network and determine their power, influence and control;

Cohesion measures reveal key relationships within the interbank market in
terms of connectivity,

Distance measures offer insight into the span of the network and how
different types of information may flow through the interbank market.
21
Centrality and distribution

Degree centrality:

The degree of a node is the number of edges connected
to that node.

In terms of the interbank network, this indicates the
number of other banks that a given bank has lending and
borrowing relationship with.

The greater the total degree of a bank, the higher is the
interconnectedness of the bank to other banks in the
system through interbank lending.
22
Centrality and distribution

Average network degree = 2.7
BANK
DEGREE
INDEGREE
OUTDEGREE
A
B
C
D
E
F
G
H
I
J
K
L
M
N
4
2
2
5
3
4
1
1
1
2
3
1
2
7
3
0
0
0
3
3
0
0
1
2
3
1
2
3
1
2
2
5
1
2
1
1
0
0
0
0
0
6
23
Centrality and distribution

Clustering coefficient:

Measures the density of connections around a single node and
enables us to determine the proportions of nearest neighbours of a
node that are linked to each other.

A measure of connectedness between a node’s neighbours

The clustering co-efficient is used to check if a certain group of
banks transact or interacts within itself, and more importantly how
this behaviour changes over time.

A high network clustering coefficient means that any two banks
that already transact with a third bank are more likely to maintain
this relationship than to establish new connections with any other
bank in the network.
24
Centrality and distribution
BANK

Average clustering
coefficient = 0.027
A
B
C
D
E
F
G
H
I
J
K
L
M
N
CLUSTERING COEFFICIENT
0.167
0.000
0.000
0.000
0.000
0.167
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.048
25
Centrality and distribution

Neighbouring banks that share mutual relations
are more likely to share the burden of a potential
default and are at the same time more likely to
suffer from contagion.
 However,
no benchmark for this measure so it’s best
to analyse it over time.
26
Centrality and distribution

Betweenness centrality:
 Defined
as the number of shortest paths from all
vertices to all others that pass through that node.
 Captures
the frequency with which a given bank lies
on the shortest path between all sets of possible
bank pairs within the sample.
27
Centrality and distribution
BANK
A
B
C
D
E
F
G
H
I
J
K
L
M
N
BETWEENNESS CENTRALITY
23.000
0.900
0.333
17.167
6.900
16.467
0.000
0.000
0.000
2.333
6.900
0.000
1.400
39.600
28
Centrality and distribution

Betweenness centrality:

Presumably, if a bank is part of many paths that connect
other banks to each other, then it is likely to have
informational or relational importance within the
networks since it is vital in connecting banks to each
other.

Captures the importance of a bank not only in the first
degree (direct) links but also in the multiple-degree
(indirect) links that connect any given pair of banks.
29
Centrality and distribution

Closeness centrality:

Closeness can be regarded as a measure of how long it
will take to spread information from one node to all
other nodes sequentially
A
measure of the speed with which information spreads
through the network from a specific bank

In the interbank network, this bank would facilitate the
efficient spread of liquidity, as well as the rapid spread of
shocks.
30
Centrality and distribution
BANK
A
B
C
D
E
F
G
H
I
J
K
L
M
N
CLOSENESS CENTRALITY
0.042
0.030
0.028
0.040
0.038
0.043
0.031
0.028
0.028
0.033
0.038
0.027
0.036
0.050
31
Centrality and distribution

Strength:
 Defined as the sum
 Determine
of a bank’s assets and liabilities.
the actual weight of each node, that is,
the size of the trades through that node.
 For
directed network, compute in-strength and out-
strength:
A
bank with high in-strength is a strong borrower, while a
bank with high out strength is a strong lender.
32
Centrality and distribution
BANK
A
B
C
D
E
F
G
H
I
J
K
L
M
N
STRENGTH
21.6
9.2
28.4
76
72.9
86.7
60
1
1
15.5
53.5
1
37.5
197.9
OUTSTRENGTH
1
9.2
28.4
76
40
66
60
1
0
0
0
0
0
49.5
INSRENGTH
20.6
0
0
0
32.9
20.7
0
0
1
15.5
53.5
1
37.5
148.4
33
Cohesion and connectivity

Network density: 0.2088

An aggregate measure of connectivity, represents the
probability of any two random banks within the market
transacting with each other.

It is computed as the number of links observed in the
network at a given time divided by the total number of
possible links.

For the interbank liability network, a high density
therefore reflects a very active interbank market with
many lending relationships amongst participants.
34
Cohesion and connectivity

Network density: 0.2088

While high network density holds the benefits of greater risk
diversification, this may not hold if the exposures exceed the level of
connectivity, thus increasing contagion risk.

The cohesion between banks that is beneficial in normal times can lead to
contagion during stressed periods.

Nevertheless, a certain level of network density must be maintained in
order to guard against the impact of contagion risk

While high density increases the network’s vulnerability to shocks,
allowing them to spread through network faster, it is possible that
depending on banks’ capital levels, the impact of the shock would be
quickly absorbed.
35
Cohesion and connectivity

Simple measures of cohesion and connectivity:
 Number of nodes
 Number of links (edges)

Cohesion measures best compared across time
since there are no widely accepted benchmarks.
36
Distance measures


Average path length and network
diameter help to identify how
quickly information is spread
through an entire network.
A reduction in these indicators
would mean two things;

Increased market efficiency regards
distribution of funding or,

Increased vulnerability to contagion
risk as a sudden shock would be
transmitted through fewer banks.
AVERAGE
PATH LENGTH
2.1
DIAMETER
4.0
37
Conclusion

The level of completeness and connectivity in the interbank market
may vary over short periods as market participants adjust to several
factors including their level of available funding, interest rates in the
interbank market, financial performance of banks, among others.

Further explore the network topology of the interbank market for both
secured and unsecured claims,

Determine the source and likelihood of initial shocks to the market and
study the distribution of losses.

Work on interbank network analysis should contribute to the
development of a stress testing framework for assessing systemic risk.
38
Network analysis aides


Gephi

https://gephi.org/

An interactive visualization and exploration open-source
platform for all kinds of networks and complex systems,
dynamic and hierarchical graphs.
NodeXL

http://nodexl.codeplex.com/

Open-source template for Microsoft® Excel® 2007, 2010 and
(possibly) 2013 that makes it easy to explore network graphs
39
REFERENCES

Allen, F and Gale, D (1998), ‘Optimal financial crises’, Journal of Finance, Vol.53 (4), pages 1,245-84

Allen, F and Gale, D (2000), ‘Financial contagion’, Journal of Political Economy, Vol.108 (1), pages 1-33

Anand, K, Gai, P, Kapadia, S, Brennan, S, Willison, M (2011), ‘A network model for financial system resilience’

Babus, A (2005), ‘Contagion risk in financial networks’, Tinbergen Institute, Erasmus Universiteit Rotterdam

Canedo, J.M.D, Martinez-Jaramillo, S, ‘Financial contagion: a network model for estimating the distribution of losses for
the financial system’

De Masi, G, Iori, G, Caldarelli, G (2008), ‘The Italian interbank network: statistical properties and a simple model’,
Department of Economics, City University, London, England

Gai, P, Haldane, A and Kadapia, S (2011), ‘Complexity, concentration and contagion’

Li, S, He, J, and Zhuang, Y (2010), ‘A network model of the interbank market’

Mistrulli, P.E (2008), ‘Assessing financial contagion in the interbank market: maximum entropy versus observed
interbank lending patterns’

‘Newman, M.E.J, ‘Random graphs as models of networks’, Santa Fe Institute

Nier, E, Yang, J, Yorulmazer, T, and Alentorn, A (2008), ‘Network models and financial stability’, Working Paper No.346,
Bank of England

Sachs, A (2010), ‘Completeness, interconnectedness and distribution of interbank exposures – a parameterised analysis
of the stability of financial networks’ Deutsche Bundesbank
40