Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk

Abstract

We characterize the evolution over time of a network of credit relations among financial agents as a system of coupled stochastic processes. Each process describes the dynamics of individual financial robustness, while the coupling results from a network of liabilities among agents. The average level of risk diversification of the agents coincides with the density of links in the network. In addition to a process of diffusion of financial distress, we also consider a discrete process of default cascade, due to the re-evaluation of agents' assets. In this framework we investigate the probability of individual defaults as well as the probability of systemic default as a function of the network density. While it is usually thought that diversification of risk always leads to a more stable financial system, in our model a tension emerges between individual risk and systemic risk. As the number of counterparties in the credit network increases beyond a certain value, the default probability, both individual and systemic, starts to increase. This tension originates from the fact that agents are subject to a financial accelerator mechanism. In other words, individual financial fragility feeding back on itself may amplify the effect of an initial shock and lead to a full fledged systemic crisis. The results offer a simple possible explanation for the endogenous emergence of systemic risk in a credit network.

Network Structure and Systemic Risk in Banking Systems

“…Methodology On the methodological side, most previous studies on contagion in financial networks have mostly focused on the stability of the financial system as a whole, either in stylized equilibrium settings (Allen and Gale, 2000;Freixas et al, 2000;Battiston et al, 2009) or in simulation studies of default cascades (Upper and Worms, 2004;Mistrulli, 2007;Elsinger et al, 2006a,b;Nier et al, 2007). Nier et al (2007) measure the average number of defaults when the institutions in the system are subject one at a time to an idiosyncratic shock which wipes out their external assets.…”

“…Studies on simulated network structures have examined the variables that affect the global level of systemic risk in the network (Nier et al, 2007;Battiston et al, 2009) such as the connectivity, concentration, capital levels, but the main results (such as the level of contagion and the role of interconnectedness) strongly depend on the details of the model and the structure of the network, which have left open whether these conclusions hold in actual banking networks. On the other hand, most of the empirical studies have only partial information on the bilateral exposures in the network, and estimate missing exposures with a maximum entropy method (Sheldon and Maurer, 1998;Upper and Worms, 2004;Wells, 2004;Elsinger et al, 2006a,b;Degryse and Nguyen, 2007).…”

Bubbles, Crashes, and the Financial Cycle: The Impact of Banking Regulation on Deep Recessions

“…Currently, our model contains only one dynamic network structure that is formed endogenously: the firm-bank network of credit relationships. This could easily be extended to include: (a) an interbank market with bank-to-bank credit relationships; (b) a model with trade-credit with firm-to-firm credit linkages; (c) an extension to explicitly address macro-prudential policy issues; (d) stress-testing of individual banks, or of the network as a whole, by tracking the domino-effects of financial contagion, see, e.g., Battiston et al (2012) for work in this direction. Online-Appendix to the paper: "Bubbles, Crashes and the Financial Cycle: The Impact of Banking Regulation on Deep Recessions"…”

Macroeconomic Policy in DSGE and Agent-Based Models Redux: New Developments and Challenges Ahead

“…Delli Gatti et al, 2005a;Dosi et al, 2013Dosi et al, , 2015Caiani et al, 2015), bankruptcy cascades (e.g. Delli Gatti et al, 2010;Battiston et al, 2012), deleveraging dynamics (e.g. Raberto et al, 2012;Seppecher and Salle, 2015), etc.…”

“…Taking a complexity theory perspective and combining network theory and agentbased model can improve financial regulation and providing early signals, which could help to avoid the occurrence of financial crises (Battiston et al, 2016). For instance, Battiston et al (2012) show that the financial network is more resilient for intermediate levels of risk diversification than for the highest one. The resilience of the banking network to liquidity shocks is studied by Gai et al (2011) developing an agent-based model of the interbank lending network where heterogenous banks are randomly connected together though unsecured claims and repo activities.…”