Network Models and Financial Stability

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Network Models and Financial Stability

• Amadeo Alentorn
• Erlend Nier
• Jing Yang
• Tanju Yorulmazer

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Greenspans open letter
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Financial System and Real Economy
Financial System
Savings
Investment
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Research questions

• How the generic structure of banking system
  affect resilience to systemic failure.
• How the resilience of the inter-bank network to
  shocks relates to the following key parameters of
  the system
• the capacity of banks to absorb shocks
• the size of inter-bank exposures
• the degree of connectivity
• the degree of concentration of the banking
  sector.

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Network approach

• Existing economics theory
• Allen and Gale (2000)
• Studied two types of network a complete
  structure and an incomplete structure.
• Nodes in a network represent banks and links
  represent financial obligations between banks.
• Results depends on the pattern of
  interconnectedness
• 1. In a complete structure, the initial impact
  of financial stress may be attenuated
• 2. An incomplete structure is more prone to
  contagion

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• Real world networks
• 1. power-law degree distribution
• 2. clustering
• 3. small degree of separation small world
  phenomenon

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Empirical studies

• Empirical research on the importance of interbank
  linkages as a channel of contagion
• Sheldon and Maurer (1998) for Switzerland
• Furfine (1999) for the US
• Upper and Worms (2000) for Germany
• Wells (2002) for the UK
• Boss, Elsinger, Summer and Thurner (2003) for
  Austria.
• Limitation no generic relationship between
  stability of a financial system and features of
  the network.

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The Eboli (2004) Framework

• Network is a directional graph, where links
  represent exposures.
• Each of N nodes (banks) is connected to a source
  (ie source of shock/loss).
• Each of the N nodes is assigned a sink
  (representing net worth).
• Flow network losses flow across a network of
  banks
• When losses reach a bank, they are absorbed by
  the sink, or flow further through inter-bank
  links.

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Extending the Eboli (2004) framework

• Identify source with banks external assets
• Introduce depositors as the second sink
• deposits are senior to interbank, in turn, senior
  to net worth
• Introduce a probability law describing likelihood
  of interbank link between any two nodes (banks)
• symmetric structures (random graph a la Erdos and
  Reiny)
• or asymmetric structures (eg power law).

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• Demonstration
• Construction of a banking system
• Construction of individual banks balance sheet
• Shock propagation
• Experiments

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• Simulation results

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Experiments

• Four parameters
• Number of nodes (N)
• Erdos-Reyni probability (p)
• Percentage of Interbank assets (w)
• Net worth (c)
• In each of the following experiments, we vary one
  parameter at a time
• In each experiment, we shock one bank at a time
  to study the default dynamics, then take average
  across all banks.

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How does bank capitalisation affect contagion?
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A multiple rounds of default scenario
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How does likelihood of interbank exposure affect
contagion?
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How does banking concentration affect contagion
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How does the size of interbank exposure affect
contagion?
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• Interdependence of the parameters

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Inter-dependence of net worth and connectivity
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Heterogeneous networks
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Summary

• Under-capitalised banks impose an externality on
  other banks in the system.
• Decreases in net worth increase the number of
  contagious defaults and that this effect is
  non-linear.
• Contagion risk first increases with the
  connectivity of the banking system, then
  decreases.
• More concentrated banking systems tend to be more
  prone to systemic meltdown ?too systemic to
  fail ?