The topology of a causal network for the Chinese financial system

The paper builds a causal network for the Chinese financial system based on the Granger causality of company risks, studies its different topologies in crisis and bull period, and applies the centrality to explain individual risk and prevent systemic risk. The results show that this causal network possesses both small-world phenomenon and scale-free property, and has a little different average distance, clustering coefficient, and degree distribution in different periods, and financial institutions with high centrality not only have large individual risk, but also are important for systemic risk immunization.     

Systemic risk on different interbank network topologies

In this paper we develop an interbank market with heterogeneous financial institutions that enter into lending agreements on different network structures. Credit relationships (links) evolve endogenously via a fitness mechanism based on agents’ performance. By changing the agent’s trust on its neighbor’s performance, interbank linkages self-organize themselves into very different network architectures, ranging from random to scale-free topologies. We study which network architecture can make the financial system more resilient to random attacks and how systemic risk spreads over the network. To perturb the system, we generate a random attack via a liquidity shock. The hit bank is not automatically eliminated, but its failure is endogenously driven by its incapacity to raise liquidity in the interbank network. Our analysis shows that a random financial network can be more resilient than a scale free one in case of agents’ heterogeneity.     

Systemic Risk Analysis of Multi-Layer Financial Network System Based on Multiple Interconnections between Banks,Firms, and Assets

Global financial systems are increasingly interconnected, and risks can spread more easily, potentially causing systemic risks. Research on systemic risk based on multi-layer financial networks is relatively scarce, and studies usually focus on only one type of risk. This paper develops a model of the multi-layer financial network system based on three types of links: firm-bank credit, asset-bank portfolio, and interbank lending, which simulates systemic risk under three risk sources: firm credit default, asset depreciation, and bank bankruptcy. The impact of the multi-layer financial network structure, default risk threshold, and bank asset allocation strategy is further explored. It has been shown that the larger the risk shock, the greater the systemic risk under different risk sources, and the risk propagation cycle tends to rise and then decline. As centralized nodes in the multi-layer financial network system, bank nodes may play both blocking and propagation roles under different risk sources. Furthermore, the multi-layer financial network system is most susceptible to bank bankruptcy risk, followed by firm credit default risk. Further research indicates that increasing the average degree of firms in the bank–firm credit network, the density of the bank-asset portfolio network, and the bank capital adequacy ratio all contribute to reducing systemic risk under the three risk sources. Additionally, the more assets a bank holds in a single market, the more vulnerable it is to the risks associated with that market.     

Network versus portfolio structure in financial systems

The question of how to stabilize financial systems has attracted considerable attentionsince the global financial crisis of 2007–2009. Recently, Beale et al. [Proc. Natl. Acad.Sci. USA 108, 12647 (2011)] demonstrated that higher portfolio diversityamong banks would reduce systemic risk by decreasing the risk of simultaneous defaults atthe expense of a higher likelihood of individual defaults. In practice, however, a bankdefault has an externality in that it undermines other banks’ balance sheets. This paperexplores how each of these different sources of risk, simultaneity risk and externality,contributes to systemic risk. The results show that the allocation of external assets thatminimizes systemic risk varies with the topology of the financial network as long as assetreturns have negative correlations. In the model, a well-known centrality measure,PageRank, reflects an appropriately defined “infectiveness” of a bank. An important resultis that the most infective bank needs not always to be the safest bank. Under certaincircumstances, the most infective node should act as a firewall to prevent large-scalecollective defaults. The introduction of a counteractive portfolio structure willsignificantly reduce systemic risk.     

Systemic Losses Due to Counterparty Risk in a Stylized Banking System

We report a study of a stylized banking cascade model investigating systemic risk caused by counterparty failure using liabilities and assets to define banks’ balance sheet. In our stylized system, banks can be in two states: normally operating or distressed and the state of a bank changes from normally operating to distressed whenever its liabilities are larger than the banks’ assets. The banks are connected through an interbank lending network and, whenever a bank is distressed, its creditor cannot expect the loan from the distressed bank to be repaid, potentially becoming distressed themselves. We solve the problem analytically for a homogeneous system and test the robustness and generality of the results with simulations of more complex systems. We investigate the parameter space and the corresponding distribution of operating banks mapping the conditions under which the whole system is stable or unstable. This allows us to determine how financial stability of a banking system is influenced by regulatory decisions, such as leverage; we discuss the effect of central bank actions, such as quantitative easing and we determine the cost of rescuing a distressed banking system using re-capitalisation. Finally, we estimate the stability of the UK and US banking systems comparing the years 2007 and 2012 by using real data.     

The topology of cross-border exposures: Beyond the minimal spanning tree approach

The recent financial crisis has stressed the need to understand financial systems as networks of interdependent countries, where cross-border financial linkages play the fundamental role. It has also been emphasized that the relevance of these networks relies on the representation of changes follow on the occurrence of stress events. Here, from series of interbank liabilities and claims over different time periods, we have developed networks of positions (net claims) between countries. Besides the Minimal Spanning Tree analysis of the time-constrained networks, a coefficient of residuality is defined to capture the structural evolution of the network of cross-border financial linkages. Because some structural changes seem to be related to the role that countries play in the financial context, networks of debtor and creditor countries are also developed. Empirical results allows to relate the network structure that emerges in the last years to the globally turbulent period that has characterized financial systems since the latest nineties. The residuality coefficient highlights an important modification acting in the financial linkages across countries in the period 1997–2011, and situates the recent financial crises as replica of a larger structural change going on since 1997.     

A network model of the interbank market

This work introduces a network model of an interbank market based on interbank credit lending relationships. It generates some network features identified through empirical analysis. The critical issue to construct an interbank network is to decide the edges among banks, which is realized in this paper based on the interbank’s degree of trust. Through simulation analysis of the interbank network model, some typical structural features are identified in our interbank network, which are also proved to exist in real interbank networks. They are namely, a low clustering coefficient and a relatively short average path length, community structures, and a two-power-law distribution of out-degree and in-degree.     

Loan and nonloan flows in the Australian interbank network

High-value transactions between banks in Australia are settled in the Reserve Bank Information and Transfer System (RITS) administered by the Reserve Bank of Australia. RITS operates on a real-time gross settlement (RTGS) basis and settles payments and transfers sourced from the SWIFT payment delivery system, the Austraclear securities settlement system, and the interbank transactions entered directly into RITS. In this paper, we analyse a dataset received from the Reserve Bank of Australia that includes all interbank transactions settled in RITS on an RTGS basis during five consecutive weekdays from 19 February 2007 inclusive, a week of relatively quiescent market conditions. The source, destination, and value of each transaction are known, which allows us to separate overnight loans from other transactions (nonloans) and reconstruct monetary flows between banks for every day in our sample. We conduct a novel analysis of the flow stability and examine the connection between loan and nonloan flows. Our aim is to understand the underlying causal mechanism connecting loan and nonloan flows. We find that the imbalances in the banks’ exchange settlement funds resulting from the daily flows of nonloan transactions are almost exactly counterbalanced by the flows of overnight loans. The correlation coefficient between loan and nonloan imbalances is about −0.9 on most days. Some flows that persist over two consecutive days can be highly variable, but overall the flows are moderately stable in value. The nonloan network is characterised by a large fraction of persistent flows, whereas only half of the flows persist over any two consecutive days in the loan network. Moreover, we observe an unusual degree of coherence between persistent loan flow values on Tuesday and Wednesday. We probe static topological properties of the Australian interbank network and find them consistent with those observed in other countries.     

Derivatives and credit contagion in interconnected networks

The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, but also by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that, by creating additional contagion channels, CDS can actually lead to greater instability of the entire network in times of economic stress. This is particularly pronounced when CDS are used by banks to expand their loan books (arguing that CDS would offload the additional risks from their balance sheets). Thus, even with complete hedging through CDS, a significant loan book expansion can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.     

The role of banks in the Brazilian interbank market: Does bank type matter?

This paper analyzes the Brazilian interbank network structure using a complex network-based approach. Results suggest a weak evidence of community structure, high heterogeneity of the network and that this market is characterized by money centers having exposures to many banks. Furthermore, we go beyond the structure of the network using information about the characteristics of the nodes and a non-parametric test in order to understand the role of the banks in the interbanking market.     

Measuring the default risk of sovereign debt from the perspective of network

Recently, there has been a growing interest in network research, especially in the fields of biology, computer science, and sociology. It is natural to address complex financial issues such as the European sovereign debt crisis from the perspective of network. In this article, we construct a network model according to the debt–credit relations instead of using the conventional methodology to measure the default risk. Based on the model, a risk index is examined using the quarterly report of consolidated foreign claims from the Bank for International Settlements (BIS) and debt/GDP ratios among these reporting countries. The empirical results show that this index can help the regulators and practitioners not only to determine the status of interconnectivity but also to point out the degree of the sovereign debt default risk. Our approach sheds new light on the investigation of quantifying the systemic risk.     

Complex networks and banking systems supervision

Comprehensive and thorough supervision of all banking institutions under a Central Bank’s regulatory control has become necessary as recent banking crises show. Promptly identifying bank distress and contagion issues is of great importance to the regulators. This paper proposes a methodology that can be used additionally to the standard methods of bank supervision or the new ones proposed to be implemented. By this, one can reveal the degree of banks’ connectedness and thus identify “core” instead of just “big” banks. Core banks are central in the network in the sense that they are shown to be crucial for network supervision. Core banks can be used as gauges of bank distress over a sub-network and promptly raise a red flag so that the central bank can effectively and swiftly focus on the corresponding neighborhood of financial institutions. In this paper we demonstrate the proposed scheme using as an example the asset returns variable. The method may and should be used with alternative variables as well.     

A model for the evaluation of systemic risk in stock markets

Systemic risk refers to the possibility of a collapse of an entire financial system or market, differing from the risk associated with any particular individual or a group pertaining to the system, which may include banks, government, brokers, and creditors. After the 2008 financial crisis, a significant amount of effort has been directed to the study of systemic risk and its consequences around the world. Although it is very difficult to predict when people begin to lose confidence in a financial system, it is possible to model the relationships among the stock markets of different countries and perform a Monte Carlo-type analysis to study the contagion effect. Because some larger and stronger markets influence smaller ones, a model inspired by a catalytic chemical model is proposed. In chemical reactions, reagents with higher concentrations tend to favor their conversion to products. In order to modulate the conversion process, catalyzers may be used. In this work, a mathematical modeling is proposed with bases on the catalytic chemical reaction model. More specifically, the Hang Seng and Dow Jones indices are assumed to dominate Ibovespa (the Brazilian Stock Market index), such that the indices of strong markets are taken as being analogous to the concentrations of the reagents and the indices of smaller markets as concentrations of products. The role of the catalyst is to model the degree of influence of one index on another. The actual data used to fit the model parameter consisted of the Hang Seng index, Dow Jones index, and Ibovespa, since 1993. “What if” analyses were carried out considering some intervention policies.     

The topology of interbank payment flows

We explore the network topology of the interbank payments transferred between commercial banks over the Fedwire^®${}^{\circledR }$ Funds Service. We find that the network has both a low average path length and low connectivity. The network includes a tightly connected core of banks to which most other banks connect. The degree distribution is scale free over a substantial range. We find that the properties of the network changed considerably in the immediate aftermath of the events of September 11, 2001.     

A Network Approach to the Study of the Dynamics of Risk Spillover in China’s Bond Market

Since 2018, the bond market has surpassed the stock market, becoming the biggest investment area in China’s security market, and the systemic risks of China’s bond market are of non-negligible importance. Based on daily interest rate data of representative bond categories, this study conducted a dynamic analysis based on generalized vector autoregressive volatility spillover variance decomposition, constructed a complex network, and adopted the minimum spanning tree method to clarify and analyze the risk propagation path between different bond types. It is found that the importance of each bond type is positively correlated with liquidity, transaction volume, and credit rating, and the inter-bank market is the most important market in the entire bond market, while interest rate bonds, bank bonds and urban investment bonds are important varieties with great systemic importance. In addition, the long-term trend of the dynamic spillover index of China’s bond market falls in line with the pace of the interest rate adjustments. To hold the bottom line of preventing financial systemic risks of China’s bond market, standard management, strict supervision, and timely regulation of the bond markets are required, and the structural entropy, as a useful indicator, also should be used in the risk management and monitoring.     

Mitigating cascades in sandpile models: an immunization strategy for systemic risk?

We use a simple model of distress propagation (the sandpile model) to show how financial systems are naturally subject to the risk of systemic failures. Taking into account possible network structures among financial institutions, we investigate if simple policies can limit financial distress propagation to avoid system-wide crises, i.e. to dampen systemic risk. We therefore compare different immunization policies (i.e. targeted helps to financial institutions) and find that the information coming from the network topology allows to mitigate systemic cascades by targeting just few institutions.     

Causality Analysis for COVID-19 among Countries Using Effective Transfer Entropy

In this study, causalities of COVID-19 across a group of seventy countries are analyzed with effective transfer entropy. To reveal the causalities, a weighted directed network is constructed. In this network, the weights of the links reveal the strength of the causality which is obtained by calculating effective transfer entropies. Transfer entropy has some advantages over other causality evaluation methods. Firstly, transfer entropy can quantify the strength of the causality and secondly it can detect nonlinear causal relationships. After the construction of the causality network, it is analyzed with well-known network analysis methods such as eigenvector centrality, PageRank, and community detection. Eigenvector centrality and PageRank metrics reveal the importance and the centrality of each node country in the network. In community detection, node countries in the network are divided into groups such that countries in each group are much more densely connected.     

Driver Countries in Global Banking Network

We analyze the network of cross-border bank lending connections among countries from 1977 to 2018. The network includes core countries that lend money and peripheral countries that borrow money from core countries. In nowadays highly connected banking network, financial crisis that start from a country can spread to other countries very fast and cause global affects. We use principal component analysis (PCA) to find the influential lending (core) countries in this network over the years and clusters of borrowing (peripheral) countries related to these impactful core countries. We find three clusters of peripheral countries, with some constant and some changing members over time. This can be a sign of changes in the financial or political interactions among countries. The changes in the role of core countries and how these roles get affected by the important financial crisis in the past decades is investigated. Among 31 of core countries, 7 countries have a partially or constantly important role in the network including France, United Kingdom, United States, Japan, Germany, Chinese Taipei and Switzerland.     

基于节点负荷失效的网络可控性研究

Liu和Barabasi将现代控制理论应用到线性系统的网络可控性问题上, 提出了最小驱动节点集的计算方法, 解决了复杂网络控制的可计算问题. 针对现实网络中存在的节点因负荷过载而失效的问题, 本文提出了基于节点负荷失效的网络可控性模型. 通过对网络采用介数和Weibull失效模型, 在随机和目标失效机制下进行仿真, 研究结果表明: 维持无标度网络可控性的难度要明显大于随机网络; 在目标节点失效机制下, 即使对网络输入极少的失效信号, 也能极大地破坏网络的可控性; 使高介数节点失效要比使度高节点失效更能破坏网络的可控性, 说明高介数节点在维持网络可控性上发挥着重要作用; 对不同的负荷失效模型, 要合理采取措施, 防止网络发生阶跃性全不可控现象. 关键词： 网络可控性 结构可控性 节点失效     

Congestion and cascades in payment systems

We develop a parsimonious model of the interbank payment system. The model incorporates an endogenous instruction arrival process, a scale-free topology of payments between banks, a fixed total liquidity which limits banks’ capacity to process arriving instructions, and a global market that distributes liquidity. We find that at low liquidity the system becomes congested and payment settlement loses correlation with payment instruction arrival, becoming coupled across the network. The onset of congestion is evidently related to the relative values of three characteristic times: the time for banks’ net position to return to 0, the time for a bank to exhaust its liquidity endowment, and the liquidity market relaxation time. In the congested regime settlement takes place in cascades having a characteristic length scale. A global liquidity market substantially attenuates congestion, requiring only a small fraction of the payment-induced liquidity flow to achieve strong beneficial effects.