Financial Contagion and Systemic Risk

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:

(Upper panel) Diagram of credit shock propagation. Bank 1 loses some assets and thus suffers equity losses; as a consequennce the loan of bank 3 to bank 1 loses values and thus also bank 3 is hit by equity losses. (Lower panel) Dynamics of contagion via overlapping portfolios. Bank 1 sells assets A and B, causing A and B to depreciate; asset values of banks 1 and 2, which hold A and B, are reduced, so that bank 2 may need to sells assets A and C, and so forth.

Funding shocks and epidemics of liquidity shortages

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.

Network stress tests for Central Counterparties

An important consequence of the global financial crisis was the establishment of a central clearing mechanism for which many bilateral contracts between banks are rerouted through a single institution, the central counterparty (CCP). Central clearing is useful to reduce systemic risk but is costly for the participating banks, as the CCP collects guarantees in the form of a default fund that is used to cover any potential insolvency of a bank. According to current regulation, the default fund should be calibrated to withstand losses resulting from the default of the two banks to which the CCP is most exposed. Such cover 2 requirement however does not take into account the effect of these defaults on the propagation of shocks over unsecured over-the-counter markets. In this paper we proposed a stress test methodology for CCPs that takes into account the propagation and amplification of financial distress through the network of bilateral exposures between banks. The model builds on a generalised DebtRank dynamics, developed in this paper, which takes into account solvency and funding contagion simultaneously. We apply the proposed framework to the fixed-income asset class of Cassa di Compensazione e Garanzia (CC&G, now Euronext clearing), the CCP operating in Italy, whose cleared securities are mainly Italian government bonds. We consider two different scenarios where exogenous losses may be incurred: a distributed initial shock and a shock corresponding to the cover 2 requirement (the simultaneous default of the two most exposed banks). As the figure shows, network effects increase substantially banks' vulnerability in both scenarios, though distress propagation is much more rapid in the latter case. Overall our results show that setting a default fund according to current regulatory standard may not be adequate for the taming of systemic events. 

Vulnerability values of banks (with different leverages) for multile round of shock propagation on the network, for the scenarios of distributed initial shocks and cover 2 shocks.

Network vs balance sheet effects on systemic risk

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.