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.     

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.     

The origins of dragon-kings and their occurrence in society

A society is a medium with a complex structure of one-to-one relations between people. Those could be relations between friends, wife–husband relationships, relations between business partners, and so on. At a certain level of analysis, a society can be regarded as a gigantic maze constituted of one-to-one relationships between people. From a physical standpoint it can be considered as a highly porous medium. Such media are widely known for their outstanding properties and effects like self-organized criticality, percolation, power-law distribution of network cluster sizes, etc. In these media supercritical events, referred to as dragon-kings, may occur in two cases: when increasing stress is applied to a system (self-organized criticality scenario) or when increasing conductivity of a system is observed (percolation scenario). In social applications the first scenario is typical for negative effects: crises, wars, revolutions, financial breakdowns, state collapses, etc. The second scenario is more typical for positive effects like emergence of cities, growth of firms, population blow-ups, economic miracles, technology diffusion, social network formation, etc. If both conditions (increasing stress and increasing conductivity) are observed together, then absolutely miraculous dragon-king effects can occur that involve most human society. Historical examples of this effect are the emergence of the Mongol Empire, world religions, World War II, and the explosive proliferation of global internet services. This article describes these two scenarios in detail beginning with an overview of historical dragon-king events and phenomena starting from the early human history till the last decades and concluding with an analysis of their possible near future consequences on our global society. Thus we demonstrate that in social systems dragon-king is not a random outlier unexplainable by power-law statistics, but a natural effect. It is a very large cluster in a porous percolation medium. It occurs as a result of changes in external conditions, such as supercritical load, increase in system elements’ sensitivity, or system connectivity growth.     

Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007–2008 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.     

Collective firm bankruptcies and phase transition in rating dynamics

We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends on the mean interaction strength. For small interaction strength parameters, there are many independent bankruptcies of individual companies. For large parameters, there are giant collective defaults of firm clusters. In the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strength of the firm’s interactions from the systemic risk point of view.     

Innovation flow through social networks: productivity distribution in France and Italy

From a detailed empirical analysis of the productivity of non financial firms across several countries and years we show that productivity follows a non-Gaussian distribution with `fat tails' in the large productivity region which are well mimicked by power law behaviors. We discuss how these empirical findings can be linked to a mechanism of exchanges in a social network where firms improve their productivity by direct innovation and/or by imitation of other firm's technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we show that the expectation values of the productivity of each firm are proportional to its connectivity in the network of links between firms. The comparison with the empirical distributions in France and Italy reveals that in this model, such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.     

Synchronizability of chaotic logistic maps in delayed complex networks

We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two regimes of synchronization, depending on the distribution of delays: when the delays are sufficiently heterogeneous the network synchronizes on a steady-state (that is unstable for the uncoupled maps); when the delays are homogeneous, it synchronizes in a time-dependent state (that is either periodic or chaotic). Using two global indicators we quantify the synchronizability on the two regimes, focusing on the roles of the network connectivity and the topology. The connectivity is measured in terms of the average number of links per node, and we consider various topologies (scale-free, small-world, star, and nearest-neighbor with and without a central hub). With weak connectivity and weak coupling strength, the network displays an irregular oscillatory dynamics that is largely independent of the topology and of the delay distribution. With heterogeneous delays, we find a threshold connectivity level below which the network does not synchronize, regardless of the network size. This minimum average number of neighbors seems to be independent of the delay distribution. We also analyze the effect of self-feedback loops and find that they have an impact on the synchronizability of small networks with large coupling strengths. The influence of feedback, enhancing or degrading synchronization, depends on the topology and on the distribution of delays.     

Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in different stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007-2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance.     

Coevolutionary Dynamics with Global Fields

We investigate the effects of external and autonomous global interaction fields on an adaptive network of social agents with an opinion formation dynamics based on a simple imitation rule. We study the competition between global fields and adaptive rewiring on the space of parameters of the system. The model represents an adaptive society subject to global mass media such as a directed opinion influence or feedback of endogenous cultural trends. We show that, in both situations, global mass media contribute to consensus and to prevent the fragmentation of the social network induced by the coevolutionary dynamics. We present a discussion of these results in the context of dynamical systems and opinion formation dynamics.     

Coherence and Entropy of Credit Cycles across the Euro Area Candidate Countries

The pattern of financial cycles in the European Union has direct impacts on financial stability and economic sustainability in view of adoption of the euro. The purpose of the article is to identify the degree of coherence of credit cycles in the countries potentially seeking to adopt the euro with the credit cycle inside the Eurozone. We first estimate the credit cycles in the selected countries and in the euro area (at the aggregate level) and filter the series with the Hodrick–Prescott filter for the period 1999Q1–2020Q4. Based on these values, we compute the indicators that define the credit cycle similarity and synchronicity in the selected countries and a set of entropy measures (block entropy, entropy rate, Bayesian entropy) to show the high degree of heterogeneity, noting that the manifestation of the global financial crisis has changed the credit cycle patterns in some countries. Our novel approach provides analytical tools to cope with euro adoption decisions, showing how the coherence of credit cycles can be increased among European countries and how the national macroprudential policies can be better coordinated, especially in light of changes caused by the pandemic crisis.     

Agreement dynamics on interaction networks with diverse topologies

We review the behavior of a recently introduced model of agreement dynamics, called the "Naming Game." This model describes the self-organized emergence of linguistic conventions and the establishment of simple communication systems in a population of agents with pairwise local interactions. The mechanisms of convergence towards agreement strongly depend on the network of possible interactions between the agents. In particular, the mean-field case in which all agents communicate with all the others is not efficient, since a large temporary memory is requested for the agents. On the other hand, regular lattice topologies lead to a fast local convergence but to a slow global dynamics similar to coarsening phenomena. The embedding of the agents in a small-world network represents an interesting tradeoff: a local consensus is easily reached, while the long-range links allow to bypass coarsening-like convergence. We also consider alternative adaptive strategies which can lead to faster global convergence.     

Quantitative agent-based firm dynamics simulation with parameters estimated by financial and transaction data analysis

Firm dynamics on a transaction network is considered from the standpoint of econophysics, agent-based simulations, and game theory. In this model, interacting firms rationally invest in a production facility to maximize net present value. We estimate parameters used in the model through empirical analysis of financial and transaction data. We propose two different methods (analytical method and regression method) to obtain an interaction matrix of firms. On a subset of a real transaction network, we simulate firm's revenue, cost, and fixed asset, which is the accumulated investment for the production facility. The simulation reproduces the quantitative behavior of past revenues and costs within a standard error when we use the interaction matrix estimated by the regression method, in which only transaction pairs are taken into account. Furthermore, the simulation qualitatively reproduces past data of fixed assets.     

Large-scale structure of a nation-wide production network

Production in an economy is a set of firms’ activities as suppliers and customers; a firm buys goods from other firms, puts value added and sells products to others in a giant network of production. Empirical study is lacking despite the fact that the structure of the production network is important to understand and make models for many aspects of dynamics in economy. We study a nation-wide production network comprising a million firms and millions of supplier-customer links by using recent statistical methods developed in physics. We show in the empirical analysis scale-free degree distribution, disassortativity, correlation of degree to firm-size, and community structure having sectoral and regional modules. Since suppliers usually provide credit to their customers, who supply it to theirs in turn, each link is actually a creditor-debtor relationship. We also study chains of failures or bankruptcies that take place along those links in the network, and corresponding avalanche-size distribution.     

Network analysis of the state space of discrete dynamical systems

We study networks representing the dynamics of elementary 1D cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54, and 110. We further define the path diversity as a global network measure. The coappearance of nontrivial scaling in both the hub size and the path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's class IV and some class III CA.     

Exploring maps with greedy navigators

During the last decade of network research focusing on structural and dynamical properties of networks, the role of network users has been more or less underestimated from the bird's-eye view of global perspective. In this era of global positioning system equipped smartphones, however, a user's ability to access local geometric information and find efficient pathways on networks plays a crucial role, rather than the globally optimal pathways. We present a simple greedy spatial navigation strategy as a probe to explore spatial networks. These greedy navigators use directional information in every move they take, without being trapped in a dead end based on their memory about previous routes. We suggest that the centralities measures have to be modified to incorporate the navigators' behavior, and present the intriguing effect of navigators' greediness where removing some edges may actually enhance the routing efficiency, which is reminiscent of Braess's paradox. In addition, using samples of road structures in large cities around the world, it is shown that the navigability measure we define reflects unique structural properties, which are not easy to predict from other topological characteristics. In this respect, we believe that our routing scheme significantly moves the routing problem on networks one step closer to reality, incorporating the inevitable incompleteness of navigators' information.     

Rates of profit as correlated sums of random variables

Profit realization is the dominant feature of market-based economic systems, determining their dynamics to a large extent. Rather than attaining an equilibrium, profit rates vary widely across firms, and the variation persists over time. Differing definitions of profit result in differing empirical distributions. To study the statistical properties of profit rates, I used data from a publicly available database for the US Economy for 2009–2010 (Risk Management Association). For each of three profit rate measures, the sample space consists of 771 points. Each point represents aggregate data from a small number of US manufacturing firms of similar size and type (NAICS code of principal product). When comparing the empirical distributions of profit rates, significant ‘heavy tails’ were observed, corresponding principally to a number of firms with larger profit rates than would be expected from simple models. An apparently novel correlated sum of random variables statistical model was used to model the data. In the case of operating and net profit rates, a number of firms show negative profits (losses), ruling out simple gamma or lognormal distributions as complete models for these data.     

Statistical mechanics of money: how saving propensity affects its distribution

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents. Received 2 May 2000     

Microscopic study reveals the singular origins of growth

Anderson [Science 177, 293 (1972)] proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with reality. In the social sciences however, the possibilities to stage experiments to validate it are limited. During the 90's a series of dramatic political and economic events have provided the opportunity to do so. We exploit the resulting empirical evidence to validate a simple agent based alternative to the classical logistic dynamics. The post-liberalization empirical data from Poland confirm the theoretical prediction that the dynamics is dominated by singular rare events which insure the resilience and adaptability of the system. We have shown that growth is led by few singular “growth centers" (Fig. 1), that initially developed at a tremendous rate (Fig. 3), followed by a diffusion process to the rest of the country and leading to a positive growth rate uniform across the counties. In addition to the interdisciplinary unifying potential of our generic formal approach, the present work reveals the strong causal ties between the “softer" social conditions and their “hard" economic consequences.