Network Models and Financial Stability

1. Network Models and Financial Stability Amadeo Alentorn Erlend Nier Jing Yang

2. Greenspan’s open letter…

3. Financial System and Real Economy Financial System Savings Investment

4. 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 capacityof banks to absorb shocks • the size of inter-bank exposures • the degree of connectivity • the degree of concentration of the banking sector.

5. 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

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

7. 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.

8. 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.

9. 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).

12. Demonstration • Construction of a banking system • Construction of individual bank’s balance sheet • Shock propagation • Experiments

13. Simulation results

14. 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.

15. How does bank capitalisation affect contagion?

16. A multiple rounds of default scenario

17. How does the size of interbank exposure affect contagion?

18. How does likelihood of interbank exposure affect contagion?

19. How does banking concentration affect contagion

20. Interdependence of the parameters

21. Inter-dependence of net worth and connectivity

22. Heterogeneous networks

23. 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 connectivityof the banking system, then decreases. • More concentrated banking systems tend to be more prone to systemic meltdown ‘too systemic to fail’ ?