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Register a new userSystemic risk governance in a dynamical model of a banking system
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We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary reserves of the banks as functions of time. The banking system model considered generalizes previous models studied in [5], [4], [7] and describes an homogeneous population of banks. Two distinct mechanisms are used to model the cooperation among banks and the cooperation between banks and monetary authority. These mechanisms are regulated respectively by the parameters $alpha$ and $gamma$. A bank fails when its log-monetary reserves go below an assigned default level. We call systemic risk or systemic event in a bounded time interval the fact that in that time interval at least a given fraction of the banks fails. The probability of systemic risk in a bounded time interval is evaluated using statistical simulation. A method to govern the probability of systemic risk in a bounded time interval is presented. The goal of the governance is to keep the probability of systemic risk in a bounded time interval between two given thresholds. The governance is based on the choice of the log-monetary reserves of a kind of ideal bank as a function of time and on the solution of an optimal control problem for the mean field approximation of the banking system model. The solution of the optimal control problem determines the parameters $alpha$ and $gamma$ as functions of time, that is defines the rules of the borrowing and lending activity among banks and between banks and monetary authority. Some numerical examples are discussed. The systemic risk governance is tested in absence and in presence of positive and negative shocks acting on the banking system.
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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.
Financial markets are exposed to systemic risk, the risk that a substantial fraction of the system ceases to function and collapses. Systemic risk can propagate through different mechanisms and channels of contagion. One important form of financial contagion arises from indirect interconnections between financial institutions mediated by financial markets. This indirect interconnection occurs when financial institutions invest in common assets and is referred to as overlapping portfolios. In this work we quantify systemic risk from indirect interconnections between financial institutions. Having complete information of security holdings of major Mexican financial intermediaries and the ability to uniquely identify securities in their portfolios, allows us to represent the Mexican financial system as a bipartite network of securities and financial institutions. This makes it possible to quantify systemic risk arising from overlapping portfolios. We show that focusing only on direct exposures underestimates total systemic risk levels by up to 50%. By representing the financial system as a multi-layer network of direct exposures (default contagion) and indirect exposures (overlapping portfolios) we estimate the mutual influence of different channels of contagion. The method presented here is the first objective data-driven quantification of systemic risk on national scales that includes overlapping portfolios.
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.
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.
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