Failure dynamics of the global risk network

Risks threatening modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about how risk materializations in distinct domains influence each other. Here we present an approach in which expert assessments of risks likelihoods and influence underlie a quantitative model of the global risk network dynamics. The modeled risks range from environmental to economic and technological and include difficult to quantify risks, such as geo-political or social. Using the maximum likelihood estimation, we find the optimal model parameters and demonstrate that the model including network effects significantly outperforms the others, uncovering full value of the expert collected data. We analyze the model dynamics and study its resilience and stability. Our findings include such risk properties as contagion potential, persistence, roles in cascades of failures and the identity of risks most detrimental to system stability. The model provides quantitative means for measuring the adverse effects of risk interdependence and the materialization of risks in the network

Systemic risk and the dynamics of temporary financial networks

This paper has two main objectives: first, to provide a formal definition of endogenous systemic risk that is firmly grounded in equilibrium dynamics of temporary financial networks (i.e., short-term lending and investment networks); and second, to construct a discounted stochastic game (DSG) model of the emergence of equilibrium network dynamics that fully takes into account the feedback between network structure, strategic behavior, and risk. Based on our definition of systemic risk we also propose a formal definition of tipping points. Using these tools we provide a strategic approach to making global assessments of systemic risk in temporary financial networks. Our approach is based on three key facts: (1) the equilibrium dynamics which emerge from the game of network formation generate finitely many disjoint basins of attraction as well as finitely many ergodic measures (implying that, starting from any temporary financial network, in finite time with probability one, the dynamic sequence of networks arrives at one of these basins, and once there, stays there), (2) each basin of attraction is homogenous with respect to its default characteristics (meaning that if a basin contains networks having a particular set of defaulted players, then all networks contained in this basin have the same set of defaulted players), and (3) the unique profile of basins generated by the equilibrium dynamics carries with it a unique set of tipping points (special networks) - and these tipping points provide an early warning of network failure

Artificial intelligence applied to bailout decisions in financial systemic risk management

We describe the bailout of banks by governments as a Markov Decision Process (MDP) where the actions are equity investments. The underlying dynamics is derived from the network of financial institutions linked by mutual exposures, and the negative rewards are associated to the banks' default. Each node represents a bank and is associated to a probability of default per unit time (PD) that depends on its capital and is increased by the default of neighbouring nodes. Governments can control the systemic risk of the network by providing additional capital to the banks, lowering their PD at the expense of an increased exposure in case of their failure. Considering the network of European global systemically important institutions, we find the optimal investment policy that solves the MDP, providing direct indications to governments and regulators on the best way of action to limit the effects of financial crises.Comment: 12 pages, 6 figure

“Price-Quakes” Shaking the World's Stock Exchanges

Background: Systemic risk has received much more awareness after the excessive risk taking by major financial instituations pushed the world’s financial system into what many considered a state of near systemic failure in 2008. The IMF for example in its yearly 2009 Global Financial Stability Report acknowledged the lack of proper tools and research on the topic. Understanding how disruptions can propagate across financial markets is therefore of utmost importance. Methodology/Principal Findings: Here, we use empirical data to show that the world’s markets have a non-linear threshold response to events, consistent with the hypothesis that traders exhibit change blindness. Change blindness is the tendency of humans to ignore small changes and to react disproportionately to large events. As we show, this may be responsible for generating cascading events—pricequakes—in the world’s markets. We propose a network model of the world’s stock exchanges that predicts how an individual stock exchange should be priced in terms of the performance of the global market of exchanges, but with change blindness included in the pricing. The model has a direct correspondence to models of earth tectonic plate movements developed in physics to describe the slip-stick movement of blocks linked via spring forces. Conclusions/Significance: We have shown how the price dynamics of the world’s stock exchanges follows a dynamics of build-up and release of stress, similar to earthquakes. The nonlinear response allows us to classify price movements of a given stock index as either being generated internally, due to specific economic news for the country in question, or externally, by the ensemble of the world’s stock exchanges reacting together like a complex system. The model may provide new insight into the origins and thereby also prevent systemic risks in the global financial network

Stability analysis of financial contagion due to overlapping portfolios

Common asset holdings are widely believed to have been the primary vector of contagion in the recent financial crisis. We develop a network approach to the amplification of financial contagion due to the combination of overlapping portfolios and leverage, and we show how it can be understood in terms of a generalized branching process. By studying a stylized model we estimate the circumstances under which systemic instabilities are likely to occur as a function of parameters such as leverage, market crowding, diversification, and market impact. Although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result financial contagion gets worse with too much diversification. Under our model there is a critical threshold for leverage; below it financial networks are always stable, and above it the unstable region grows as leverage increases. The financial system exhibits "robust yet fragile" behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. Our model and methods of analysis can be calibrated to real data and provide simple yet powerful tools for macroprudential stress testing.Comment: 25 pages, 8 figure

Systemic Risk in a Unifying Framework for Cascading Processes on Networks

We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure

How big is too big? Critical Shocks for Systemic Failure Cascades

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure