Financial asset bubbles in banking networks

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly asset. The banks in the periphery have not direct access to the bubble, but can take initially advantage from its increase by investing on the banks in the core. Investments are modeled by the weight of the links, which is a function of the robustness of the banks. In this way, a preferential attachment mechanism towards the core takes place during the growth of the bubble. We then investigate how the bubble distort the shape of the network, both for finite and infinitely large systems, assuming a non vanishing impact of the core on the periphery. Due to the influence of the bubble, the banks are no longer independent, and the law of large numbers cannot be directly applied at the limit. This results in a term in the drift of the diffusions which does not average out, and that increases systemic risk at the moment of the burst. We test this feature of the model by numerical simulations.Comment: 33 pages, 6 table

Volatility co-movements and spillover effects within the Eurozone economies: A multivariate GARCH approach using the financial stress index

The Eurozone crisis is one the most important economic event in recent years. At its peak, the effects of the crisis have put at serious risk the outcome of the euro project, exposing the inherent weaknesses and vulnerabilities of the monetary union. As the degree of economic and financial integration of these countries is significant, we aim to investigate in details the potential cross-covariance and spillover effects between the Eurozone economies and financial markets. In order to do this, we employ financial stress indexes, as systemic risk metrics in a multivariate GARCH model. This method is able to capture markets’ dependencies and volatility spillovers and is employed on a single market level as well as on the full spectrum of Eurozone markets. The empirical results have shown the important and intensive stress transmission on banking and money markets. Moreover, the role of peripheral countries as stress transmitter is verified, but only for particular periods. The significant spillover effects from core countries are also evident, indicating their important role in the Euro Area and its overall financial stability. The “decoupling” hypothesis is empirically verified, underling the gradually decreasing intensity of spillovers between Euro Area countries. Overall, this paper exhibits the complex structure of spillover effects for Eurozone, along with a clustering effect in the most recent times

Generalized Network Dismantling

Finding the set of nodes, which removed or (de)activated can stop the spread of (dis)information, contain an epidemic or disrupt the functioning of a corrupt/criminal organization is still one of the key challenges in network science. In this paper, we introduce the generalized network dismantling problem, which aims to find the set of nodes that, when removed from a network, results in a network fragmentation into subcritical network components at minimum cost. For unit costs, our formulation becomes equivalent to the standard network dismantling problem. Our non-unit cost generalization allows for the inclusion of topological cost functions related to node centrality and non-topological features such as the price, protection level or even social value of a node. In order to solve this optimization problem, we propose a method, which is based on the spectral properties of a novel node-weighted Laplacian operator. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens new directions in understanding the vulnerability and robustness of complex systems.Comment: 6 pages, 5 figure

Measuring sovereign contagion in Europe

This paper analyzes sovereign risk shift-contagion, i.e. positive and significant changes in the propagation mechanisms, using bond yield spreads for the major eurozone countries. By emphasizing the use oftwo econometric approaches based on quantile regressions (standard quantile regression and Bayesianquantile regression with heteroskedasticity) we find that the propagation of shocks in euro\u2019s bond yieldspreads shows almost no presence of shift-contagion in the sample periods considered (2003\u20132006,Nov. 2008\u2013Nov. 2011, Dec. 2011\u2013Apr. 2013). Shock transmission is no different on days with big spreadchanges and small changes. This is the case even though a significant number of the countries in our sample have been extremely affected by their sovereign debt and fiscal situations. The risk spillover amongthese countries is not affected by the size or sign of the shock, implying that so far contagion has remainedsubdued. However, the US crisis does generate a change in the intensity of the propagation of shocks inthe eurozone between the 2003\u20132006 pre-crisis period and the Nov. 2008\u2013Nov. 2011 post-Lehman one,but the coefficients actually go down, not up! All the increases in correlation we have witnessed overthe last years come from larger shocks and the heteroskedasticity in the data, not from similar shockspropagated with higher intensity across Europe. These surprising, but robust, results emerge becausethis is the first paper, to our knowledge, in which a Bayesian quantile regression approach allowing forheteroskedasticity is used to measure contagion. This methodology is particularly well-suited to dealwith nonlinear and unstable transmission mechanisms especially when asymmetric responses to signand size are suspected

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