Network Modeling 101For Financial Interlinkages

By Prajakta Kharkar-Nigam

(pkharkar@gmail.com)

Financial Stability Dept.

Bank of Uganda

22 March 2013

Acknowledgement: The presenter would like to thank Dr. Giorgos Cheliotis’ for inputs drawn from his social network analysis course at National University of Singapore

Key Question: Interconnectedness

If one bank were to face an adverse shock, how would the rest of the

system be affected?

Potential Solution:

Analysis using network modeling tools

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What does a network model look like?

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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-of-friends

• Epidemiologists track spread of diseases

• Central Banks for mapping interlinkages between FIs 4

Why Networks?

• Among central banks, who is using them?– Bank of England , Deutsche Bundesbank, European Central

Bank, Reserve Bank of India, South African Reserve Bank, Bank of Uganda etc.

• Most central banks favour network analysis because– Networks make ‘big things visible to the naked eye’

• 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 systemic shocks, contagion and crises.

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Key attributes of a network

• How to represent interlinkages in a visual map?Network map

• How to identify strong/weak interlinkages?

• How much liquidity/information is being carried through each link?

Tie strength (link perspective)

• Which nodes are critical to the network?

• Which banks are systemically important?Key players

• How close knit is the network?

• Who is likely to help/hurt who in a crisis or in the event of a bank resolution?

Cohesion (cluster perspective)

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Nodes, Links and Adjacency

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Adding magnitudes to linkages

Edges represent :• Volume, frequency or value of actual transactions •flows of information or money,•ownership affiliations

Weights (for linkages) can be based on:•Volume, frequency or value of transactions supplied by a bank•Perceptions of bank’s risk in the market •Combination

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Paths, shortest paths, longest distance

• Path: A path between any two nodes isany sequence of non-repeating nodesthat connects the two nodes.

• Shortest Path: The shortest path ordistance between two nodes is the paththat connects the two nodes with theshortest number of edges.

• Longest distance: The longest shortestpath or distance between any two nodesis a useful measure of the reach of thenetwork. It also indicates how long it willtake at most to reach any node in thenetwork.

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Tie strength and its measures• Once a network is mapped, to find out which link(s)

matters the most or is ‘central’

• Four measures of centrality:1. Degree– For identifying which banks are most connected

directly and hence, central for spreading liquidity

– Measured by number of links leading in or out of the node

2. Betweeness– For identifying which bank is systemically important

enough (well connected directly and indirectly) that if it fails, the network may either break down or will face severe delays in transferring funds

– Likewise it also tells us which banks will lead to fastest transmission of contagion risk

– Measured by number of shortest paths that pass through the given node divided by all shortest paths in the network

Degree

Betweeness

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Tie strength and its measures (cont’d)3. Closeness (double edged sword)– For identifying if we were to add liquidity in the

system, through which banks will it spread the fastest

– Likewise, if there were a panic, through which banks might it spread the fastest

– Measured by mean length of all shortest paths from a node to all other nodes in the network, that is how many hops on average does it take to reach every other node in the network

4. Eigenvector – For identifying which banks are directly

connected to the most connected banks. First round of banks to fail if a shock were to hit the well-connected node.

– Measured as proportional to sum of all the eigenvector centralities of all nodes directly connected to it.

– This is similar to how Google ranks web pages, those linked to other highly linked pages come out higher in the search results.

Closeness

Eigenvector

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Interpretation of tie strength measures for banking industry

•How many banks can this particular bank affect directly?Degree

•How likely is this bank to be systemically important to the network?Betweeness

•How quickly on average can problems at this bank spread to other banks in the network?Closeness

•How well is this bank connected to other systemically important banks?Eigenvector

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(Sets of) Key Players

•Node 10 is the most central according to degree, but nodes 3 and 5 together will reach more nodes due to closeness.

•Moreover the tie between them is critical; if severed, the network will break into two isolated sub-networks

•So other things being equal, banks 3 and 5 together are more ‘key’ to this network than bank 10

•Thinking about sets of key players is necessary

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Cohesion (cluster) and its measures• Four measures of cohesion:

1. Reciprocity:

• For identifying which banks are transacting with each other and where the relations are unilateral.

• Insight into distribution of power and dependence.

• The ratio of the number of relations which are reciprocated (i.e. there is an edge in both directions) over the total number of relations in the network

2. Density

• It is a common measure of how well connected a network is (not a specific node). A perfectly connected network is called a clique and has density=1

• Measured by the ratio of the number of edges in the network over the total number of possible edges between all pairs of nodes

Reciprocity

Density

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Cohesion and its measures (cont’d)

3. Clustering

– Clustering indicative of the presence of different smaller networks within a large network of banks.

– Indicates if certain group of banks transact or interact within themselves, and more importantly how that changes over time.

– A node’s clustering coefficient is measured as the density of its neighborhood.

4. Average distance

– For identifying how quickly on average would any shock spread through the entire banking network.

– The average of all shortest paths in a network indicates how far apart any two nodes will be on average

Clustering

Avg. distance

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Interpretation of cohesion measures for banking industry

•Which banks are transacting with each other on both sides of transactions?Reciprocity

•How close knit the banking industry is? This can cause risks to become systemic in no time.Density

• Is a certain group of banks transacting amongst themselves, and more importantly how is that changing over time?

Clustering

•How quickly on average would any shock spread through the entire banking network?

Average distance

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Further food for thought

• Network models can be used for stress testing, crisis simulation and for surveillance

• Network maps give us a framework to dissect interconnectedness with the full big picture in view.

• Key insights for macroprudential policy – Interconnectedness is a double edged sword– What is good in normal times is precisely what leads to

crises in stressed times– Optimal level of network measures is required, an excess

in either direction would be undesirable.

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The END Beginning