Credit Risk in Interbank Networks

ABSTRACT

One of the most striking characteristics of modern financial systems is their complex interdependence, comprising a network of bilateral exposures in the interbank market, in which institutions with surplus liquidity can lend to those with a liquidity shortage. Empirical studies reveal that some interbank networks have features of scale-free networks. We explore the characteristics of financial contagion in networks whose distribution of links approaches a power law, using a model that defines banks’ balance sheets from information on network connectivity. By varying the parameters for the creation of the network, several interbank networks are built, in which the concentration of debt and credit comes from the distribution of links. The results suggest that networks that are more connected and have a high concentration of credit are more resilient to contagion than other types of networks analyzed.

KEY WORDS:

• complex networks
• contagion
• financial crashes
• interbank exposure
• power laws
• systemic risk

Notes

^1. Recall, however, that other interbank networks do not present scale-free characteristics (on the e-MID electronic money market, see, e.g., Fricke and Lux 2015).

^2. More recent studies have emphasized core-periphery structures as relevant mechanisms in interbank network formation (Craig and Von Peter 2014; Fricke and Lux 2015). In such models, the idea is that banks organize themselves around a core of intermediaries, giving rise to a hierarchical structure (interbank tiering).

^3. In this work, the simulations performed use an initial network, G0, consisting of two nodes, 0 and 1, connected by two directed links, 0 → 1 and 1 → 0.

^4. For α + γ = 0.75, we have β = 0.25. Since β is the probability of creating a link without addition of a new node, we cannot use a value of β that is too small, otherwise we will have a network with very low average connectivity. However, we would like to have values of α and γ high enough to create asymmetry between the distribution of in-degree and out-degree. The values α + γ = 0.75 and β = 0.25 satisfy those requirements.

^5. The exponent of a power-law distribution reflects the concentration of the distribution: A smaller absolute value of the exponent corresponds to a more concentrated distribution. Therefore, differences between exponents X_IN and X_OUT represent differences between the concentrations of the in- and out-degree distributions.

^6. The concentration of assets in real networks is also quite high, as reported in the literature. For example, Elsinger, Lehar, and Summer (2006) report a Gini coefficient of 0.88 for the Austrian network in 2002, and Ennis (2001) reports a Gini coefficient of 0.90 for the United States in 2000.

^7. The equation for DI_i excludes from its computation the value of initial impact (NBA_i), representing only the losses due to contagion.