Nowadays the total value of the global financial market has largely exceeded the value of the real economy, as financial institutions have created a global network of interconnections and interdependencies through various financial instruments and contractual forms. Modelling the financial system as a network is thus a precondition for understanding and managing a wide range of phenomena that are relevant not only for financial professionals and economists but also for the whole society, as reflected in the speech and policy action of the highest financial authorities (see for example here, here and here).

In particular, the interconnections between financial institutions (banks, for short) have significantly increased the fragility of the system. Indeed while higher diversification reduces portfolio risk at the individual bank level, it also creates more channels for the propagation of financial losses. For example, if the price of a certain asset collapses, not only the banks that have invested in that asset are affected, but also those that have invested in the bonds of the aforementioned banks. Because of the complex contract chains and feedback mechanisms, the resulting effects can be much larger than the initial shocks. This is the so-called systemic risk, whereby due to the interconnections of the system, the failure of a single bank can cause a cascade of bankruptcies, which could potentially leading to the collapse of the entire system. The importance of such mechanisms was particularly clear in the failure of Lehman Brothers that triggered the global financial crisis of 2007-2008.

Representing the financial system as a network therefore allows us to explicitly model the propagation of shocks between banks. The idea is to describe each bank using state variables representing their balance sheet figures. When an external shock hits the system, bank variables are updated via dynamic equations that depend strongly on the network of bilateral exposures between banks. For interbank markets we can model different contagion mechanisms:

• Liquidity contagion happens when a bank fails to meet its payment obligations, because it did not receive enough payments from other banks and cannot compensate with its liquidity reserves (as in the Eisenberg and Noe model).

• Solvency contagion occurs when the reduction in creditworthiness of a bank causes losses for its creditors. Contagion in this case can happen when a bank defaults or, more generally, when its probabilities of default increases (as in the DebtRank model), due to the accounting requirement of marking assets to market. 

• Funding contagion takes place when a bank decides to hoard liquidity by not renewing its loan to another banks once it expires. If the latter bank cannot roll-over its debt with another bank, it is forced to sell its illiquid assets at a discount and book losses.

The contagion dynamics in a financial network is similar in spirit to the spreading of an epidemic within a population. In this paper we exploited this analogy to develop a model where liquidity shortages of a bank propagate as funding shocks over a network of interbank loans. When applied to eMID (electronic market for interbank deposits) data, the model reveals that the individual riskiness of a bank is better captured by its network centrality than by its participation to the market, a concept known as too interconnected to fail. As we discuss in this paper, the proposed approach represents an effective modelling based on a simplification of funding contagion dynamics, which is able to provide useful insights on systemic risk and can be successfully used as a viable alternative to more realistic but complicated models—which not only require more specific balance sheet variables with high time resolution but also need assumptions on how banks respond to liquidity shocks.

As explained above, financial networks arise because of interconnections between the balance sheets of banks. One could then ask what is the level of systemic risk that is due to the topological details of the underlying network, with respect to the risk that is inherent to the exposures of banks in the market, namely their balance sheet  composition. Using generalised DebtRank dynamics, in this paper we compared the observed systemic risk on e-MID network data with the expected systemic risk of a null model network, obtained through a grand canonical maximum-entropy approach constraining relevant balance sheet variables. We show that the aggregate levels of observed and expected systemic risks are usually compatible but differ significantly during turbulent times: after the default of Lehman Brothers in 2009 and the VLTRO implementation by the European Central Bank in 2012. At the individual level instead, banks are typically more or less risky than what their balance sheet prescribes due to their position in the network. These results confirm on one hand that balance sheet information can be effectively used to reconstruct the network and get good estimates of aggregate systemic risk. On the other hand they show the importance of knowing the empirical details of the network for conducting precise stress tests on individual banks, especially when during systemic events, when it matters the most.