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We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model could be transferred to a death process problem represented by balls-and-bins model. We also reduce the dimension of the problem by classifying banks according to different types, in an appropriate type space. These types may be calibrated to real-world data by using machine learning techniques. We then state various limit theorems regarding the final size of default cascade over different types. In particular, under suitable assumptions on the degree and threshold distributions, we show that the final size of default cascade has asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions and show how the systemic risk measure, in a given stress test scenario, could be related to the structure and heterogeneity of financial networks. We finally show how these results could be used by a social planner to optimally target interventions during a financial crisis, with a budget constraint and under partial information of the financial network.
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We discuss the systemic risk implied by the interbank exposures reconstructed with the maximum entropy method. The maximum entropy method severely underestimates the risk of interbank contagion by assuming a fully connected network, while in reality the structure of the interbank network is sparsely connected. Here, we formulate an algorithm for sparse network reconstruction, and we show numerically that it provides a more reliable estimation of the systemic risk.
Groups of enterprises can serve as guarantees for one another and form complex networks when obtaining loans from commercial banks. During economic slowdowns, corporate default may spread like a virus and lead to large-scale defaults or even systemic financial crises. To help financial regulatory authorities and banks manage the risk associated with networked loans, we identified the default contagion risk, a pivotal issue in developing preventive measures, and established iConVis, an interactive visual analysis tool that facilitates the closed-loop analysis process. A novel financial metric, the contagion effect, was formulated to quantify the infectious consequences of guarantee chains in this type of network. Based on this metric, we designed and implement a series of novel and coordinated views that address the analysis of financial problems. Experts evaluated the system using real-world financial data. The proposed approach grants practitioners the ability to avoid previous ad hoc analysis methodologies and extend coverage of the conventional Capital Accord to the banking industry.
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and risk contribution measures in terms of the VaR and ES as special cases. Sufficient conditions are presented for two random vectors to be ordered by the proposed CoD-risk measures and distortion risk contribution measures. These conditions are expressed using the conventional stochastic dominance, increasing convex/concave, dispersive, and excess wealth orders of the marginals and canonical positive/negative stochastic dependence notions. Numerical examples are provided to illustrate our theoretical findings. This paper is the second in a triplet of papers on systemic risk by the same authors. In cite{DLZorder2018a}, we introduce and analyze some new stochastic orders related to systemic risk. In a third (forthcoming) paper, we attribute systemic risk to the different participants in a given risky environment.
A growing body of studies on systemic risk in financial markets has emphasized the key importance of taking into consideration the complex interconnections among financial institutions. Much effort has been put in modeling the contagion dynamics of financial shocks, and to assess the resilience of specific financial markets - either using real network data, reconstruction techniques or simple toy networks. Here we address the more general problem of how shock propagation dynamics depends on the topological details of the underlying network. To this end we consider different realistic network topologies, all consistent with balance sheets information obtained from real data on financial institutions. In particular, we consider networks of varying density and with different block structures, and diversify as well in the details of the shock propagation dynamics. We confirm that the systemic risk properties of a financial network are extremely sensitive to its network features. Our results can aid in the design of regulatory policies to improve the robustness of financial markets.
Systemic risk arises as a multi-layer network phenomenon. Layers represent direct financial exposures of various types, including interbank liabilities, derivative- or foreign exchange exposures. Another network layer of systemic risk emerges through common asset holdings of financial institutions. Strongly overlapping portfolios lead to similar exposures that are caused by price movements of the underlying financial assets. Based on the knowledge of portfolio holdings of financial agents we quantify systemic risk of overlapping portfolios. We present an optimization procedure, where we minimize the systemic risk in a given financial market by optimally rearranging overlapping portfolio networks, under the constraints that the expected returns and risks of the individual portfolios are unchanged. We explicitly demonstrate the power of the method on the overlapping portfolio network of sovereign exposure between major European banks by using data from the European Banking Authority stress test of 2016. We show that systemic-risk-efficient allocations are accessible by the optimization. In the case of sovereign exposure, systemic risk can be reduced by more than a factor of two, with- out any detrimental effects for the individual banks. These results are confirmed by a simple simulation of fire sales in the government bond market. In particular we show that the contagion probability is reduced dramatically in the optimized network.
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