Network Models and Financial Stability Amadeo Alentorn Erlend
Network Models and Financial Stability Amadeo Alentorn Erlend Nier Jing Yang
Greenspan’s open letter…
Financial System and Real Economy Savings Financial System Investment
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: n the capacity of banks to absorb shocks n the size of inter-bank exposures n the degree of connectivity n the degree of concentration of the banking sector.
Network approach Existing economics theory: Allen and Gale (2000) n Studied two types of network: a ‘complete structure’ and an ‘incomplete structure’. n Nodes in a network represent banks and links represent financial obligations between banks. n 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
Real world networks : 1. power-law degree distribution 2. clustering 3. small degree of separation: small world phenomenon
Empirical studies Empirical research on the importance of interbank linkages as a channel of contagion: n n n 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.
The Eboli (2004) Framework n n n 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.
Extending the Eboli (2004) framework n n n Identify source with banks’ external assets Introduce depositors as the second sink n 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) n symmetric structures (random graph a la Erdos and Reiny) n or asymmetric structures (eg power law).
Demonstration n n Construction of a banking system Construction of individual bank’s balance sheet Shock propagation Experiments
Simulation results
Experiments Four parameters: n Number of nodes (N) n Erdos-Reyni probability (p) n Percentage of Interbank assets (w) n Net worth (c) n In each of the following experiments, we vary one parameter at a time; n In each experiment, we shock one bank at a time to study the default dynamics, then take average across all banks.
How does bank capitalisation affect contagion? weakly monotonic and negative relationship between bank capitalisation and contagion n contagion does not decrease linearly in bank capitalisation n for low values of net worth, a slight decrease in net worth leads to a sharp increase in number of n
A multiple rounds of default scenario
How does the size of interbank exposure affect contagion? A decrease in the percentage of external assets has two opposing effects: shock propagation and shock absorption n When the net worth is still sufficiently small, the shock propagation dominates the shock absorption. n Nonlinear relationship: for different levels of percentage of external assets, a banking system can achieve same level of resilience. n
How does likelihood of interbank exposure affect contagion? Interbank connections have two opposing effects: shock-transmitter and shock-absorber. n two mechanisms dominate over different ranges, generating an Mshaped graph. n an interesting dynamic between interbank linkages and net worth n
How does banking concentration affect contagion risk monotonically increases in size of the shock regardless of concentration level. n The more concentrated is the banking system, a higher risk of contagion for same shock. n
Interdependence of the parameters
Inter-dependence of net worth and connectivity
Heterogeneous networks n Nonlinearity: as the degree of centrality increases, contagious defaults first increase, but then start to decrease, as the number of connections to the central node start to lead to greater dissipation of the shock.
Summary n n 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 nonlinear. 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’ ?
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