Contagion and Bank Runs in a Multi-Agent Financial System

In this work we explore contagion from one institution to another that can stem from the existence of a network of financial contracts. In fact, in modern financial systems, an intricate web of claims and obligations links the balance sheets of a wide variety of intermediaries (banks, for instance) into a network structure of interdependencies that have created an environment for feedback elements to generate amplified responses to shocks to the financial system. Small shocks, which initially affect only a few institutions, can indeed spread by contagion to the rest of the financial sector and cause a crisis in the connected intermediaries. Whether the financial crisis does spread depends crucially on the patterns of interconnections generated by the cross holdings of claims. At the same time, because of agents’ incomplete information about their environment, a shock in one institution may be read as a signal predicting a shock in another institution and induce depositors, at any or all of the banks, to withdraw their funds even though bank’s fundamentals are strong. Thus, a crisis in one bank can create a self-fulfilling expectation of a crisis in another bank and lead to bank runs, which are a common feature of extreme crises. Understanding the relation between the structure of financial networks and their exposure to shocks becomes, therefore, an important issue for central banks and policy makers to assess the potential for contagion arising from the behavior of financial institutions under distress and the herd behavior of consumers. In the present work, the intricate web of claims and obligations linking the balance sheets of financial institutions and consumers’ behavior have been modeled in a structure that reflects the complexities of observed financial networks and the diffusion of crisis expectations. In particular, we make clear the network of claims and obligations linking financial institutions and provide an explicit characterization of balance sheets also in terms of reserve and leverage constraints imposed by regulators. We also relate to the ant colony model of Kirman’s to describe the behavior of consumers. In the spirit of complex system analysis, our aim is to investigate the relation between the structure of a financial network, i.e. the size and the pattern of obligations, and its exposure to default contagion with reference to different network structures. Thus, simulations have been run for several regular (complete and incomplete), and irregular (random, scale-free and star-shaped) financial networks whose performances have been investigated with reference to two parameters: the total number of depositors’ withdrawals before the system defaults, WTD, and the time the network of interconnections takes to involve all the banks in the financial crisis, TTD. Results clearly show that, when financial contagion is partially due to bank runs, an increase in the degree of interconnection worsen the system performances both in terms of WTD and TTD and unambiguously increases the risk of default. Yet, asymmetric financial structures perform much better than symmetric ones.