Dynamic models of systemic risk and contagion

Modern financial systems are complicated networks of interconnected financial institutions and default of any of them may have serious consequences for others. The recent crises have shown that complexity and interconnectedness are the major factors of systemic risk, which became the subject of intensive studies usually concentrated on static models. The authors develop a dynamic model based on the so-called structural approach, where defaults are triggered by the exit of some stochastic process from a domain. In the case considered, this is a process defined by the evolution of bank's portfolios values. At the exit time, a bank defaults and a cascade of defaults starts. The authors believe that the distribution of the exit time and the subsequent losses may serve as indicators allowing regulators to monitor the state of the system and take corrective actions in order to avoid contagion in a financial system. The authors model the development of a financial system as a random graph using the preferable attachment algorithm and provide results of numerical experiments on simulated data.