Abstract

The Statistical Physics of Complex Networks has recently provided new theoretical tools for policy makers. Here we extend the notion of network controllability to detect the financial institutions, i.e. the drivers, that are most crucial to the functioning of an interbank market. The system we investigate is a paradigmatic case study for complex networks since it undergoes dramatic structural changes over time and links among nodes can be observed at several time scales. We find a scale-free decay of the fraction of drivers with increasing time resolution, implying that policies have to be adjusted to the time scales in order to be effective. Moreover, drivers are often not the most highly connected “hub” institutions, nor the largest lenders, contrary to the results of other studies. Our findings contribute quantitative indicators which can support regulators in developing more effective supervision and intervention policies.

Abstract

The recent credit crisis of 2007/08 has raised a debate about the so-called knife-edge properties of financial markets. The paper contributes to the debate shedding light on the controversial relation between risk-diversification and financial stability. We model a financial network where assets held by borrowers to meet their obligations, include claims against other borrowers and securities exogenous to the network. The balance-sheet approach is conjugated with a stochastic setting and by a mean-field approximation the law of motion of the system's fragility is derived. We show that diversification has an ambiguous effect and beyond a certain levels elicits financial instability. Moreover, we find that risk-sharing restrictions create a socially preferable outcome. Our findings have significant implications for future policy recommendation.

Abstract

In this paper we present a novel method to reconstruct global topological properties of a complex network starting from limited information. We assume to know for all the nodes a non-topological quantity that we interpret as fitness. In contrast, we assume to know the degree, i.e. the number of connections, only for a subset of the nodes in the network. We then use a fitness model, calibrated on the subset of nodes for which degrees are known, in order to generate ensembles of networks. Here, we focus on topological properties that are relevant for processes of contagion and distress propagation in networks, i.e. network density and k-core structure, and we study how well these properties can be estimated as a function of the size of the subset of nodes utilized for the calibration. Finally, we also study how well the resilience to distress propagation in the network can be estimated using our method. We perform a first test on ensembles of synthetic networks generated with the Exponential Random Graph model, which allows to apply common tools from statistical mechanics. We then perform a second test on empirical networks taken from economic and financial contexts. In both cases, we find that a subset as small as 10 % of nodes can be enough to estimate the properties of the network along with its resilience with an error of 5 %.

Abstract

The intrinsic complexity of the financial derivatives market has emerged as both an incentive to engage in it, and a key source of its inherent instability. Regulators now faced with the challenge of taming this beast may find inspiration in the budding science of complex systems.

Abstract

Understanding something of the complexity of a financial network is one thing, influencing the behaviour of that system is another. But new tools from network science define a notion of 'controllability' that, coupled with 'centrality', could prove useful to economists and financial regulators.

Abstract

We analyse time series of CDS spreads for a set of major US and European institutions on a pe-riod overlapping the recent financial crisis. We extend the existing methodology of $$epsilon-drawdowns to the one of joint $$epsilon-drawups, in order to estimate the conditional probabilities of abrupt co-movements among spreads. We correct for randomness and for finite size effects and we find significant prob-ability of joint drawups for certain pairs of CDS. We also find significant probability of trend rein-forcement, i.e. drawups in a given CDS followed by drawups in the same CDS. Finally, we take the matrix of probability of joint drawups as an estimate of the network of financial dependencies among institutions. We then carry out a network analysis that provides insights into the role of systemically important financial institutions.

Abstract

The recent credit crisis of 2007/08 has raised a debate about the so-called knife-edge properties of financial markets. The paper contributes to the debate shedding light on the controversial relation between risk-diversification and financial stability. We model a financial network where assets held by borrowers to meet their obligations, include claims against other borrowers and securities exogenous to the network. The balance-sheet approach is conjugated with a stochastic setting and by a mean-field approximation the law of motion of the system's fragility is derived. We show that diversification has an ambiguous effect and beyond a certain levels elicits financial instability. Moreover, we find that risk-sharing restrictions create a socially preferable outcome. Our findings have significant implications for future policy recommendation.

Abstract

Building on previous works on business fluctuations, we model the propagation of financial distress in a network of regions, each populated by heterogeneous inter-acting firms and banks. In order to diversify risk, firm sell goods outside their own region and borrow from banks located there. However, this results in ties across regions which propagate financial distress across regional borders. We investigate how the average level of economic integration affects the probability of both individual and systemic failures. We find that the benefit of greater diversification is eventually offset by the effect of financial acceleration and contagion. In particular, beyond a certain level of integration the economy suffers more frequently from events with larger numbers of simultaneous failures.

Abstract

We live in a computerized and networked society where many of our actions leave a digital trace and affect other people's actions. This has lead to the emergence of a new data-driven research field: mathematical methods of computer science, statistical physics and sociometry provide insights on a wide range of disciplines ranging from social science to human mobility. A recent important discovery is that search engine traffic (i.e., the number of requests submitted by users to search engines on the www) can be used to track and, in some cases, to anticipate the dynamics of social phenomena. Successful examples include unemployment levels, car and home sales, and epidemics spreading. Few recent works applied this approach to stock prices and market sentiment. However, it remains unclear if trends in financial markets can be anticipated by the collective wisdom of on-line users on the web. Here we show that daily trading volumes of stocks traded in NASDAQ-100 are correlated with daily volumes of queries related to the same stocks. In particular, query volumes anticipate in many cases peaks of trading by one day or more. Our analysis is carried out on a unique dataset of queries, submitted to an important web search engine, which enable us to investigate also the user behavior. We show that the query volume dynamics emerges from the collective but seemingly uncoordinated activity of many users. These findings contribute to the debate on the identification of early warnings of financial systemic risk, based on the activity of users of the www.

Abstract

Systemic risk, here meant as the risk of default of a large portion of the financial system, depends on the network of financial exposures among institutions. However, there is no widely accepted methodology to determine the systemically important nodes in a network. To fill this gap, we introduce, DebtRank, a novel measure of systemic impact inspired by feedback-centrality. As an application, we analyse a new and unique dataset on the USD 1.2 trillion FED emergency loans program to global financial institutions during 2008-2010. We find that a group of 22 institutions, which received most of the funds, form a strongly connected graph where each of the nodes becomes systemically important at the peak of the crisis. Moreover, a systemic default could have been triggered even by small dispersed shocks. The results suggest that the debate on too-big-to-fail institutions should include the even more serious issue of too-central-to-fail.

Abstract

We explore the dynamics of default cascades in a network of credit interlink-ages in which each agent is at the same time a borrower and a lender. When some counterparties of an agent default, the loss she experiences amounts to her total exposure to those counterparties. A possible conjecture in this context is that individual risk diversification across more numerous counterparties should make also systemic defaults less likely. We show that this view is not always true. In particular, the diversification of credit risk across many borrowers has ambiguous effects on systemic risk in the presence of mechanisms of loss amplifications such as in the presence of potential runs among the short-term lenders of the agents in the network.

Abstract

We model the systemic risk associated with the so-called balance-sheet amplification mechanism in a system of banks with interlocked balance sheets and with positions in real-economy-related assets. Our modeling framework integrates a stochastic price dynamics with an active balance-sheet management aimed to maintain the Value-at-Risk at a target level. We find that a strong compliance with capital requirements, usually alleged to be procyclical, does not increase systemic risk unless the asset market is illiquid. Conversely, when the asset market is illiquid, even a weak compliance with capital requirements increases significantly systemic risk. Our findings have implications in terms of possible macro-prudential policies to mitigate systemic risk.

Abstract

The recent financial crisis poses the challenge to understand how systemic risk arises endogenously and what architecture can make the financial system more resilient to global crises. This paper shows that a financial network can be most resilient for intermediate levels of risk diversification, and not when this is maximal, as generally thought so far. This finding holds in the presence of the financial accelerator, i.e. when negative variations in the financial robustness of an agent tend to persist in time because they have adverse effects on the agent's subsequent performance through the reaction of the agent's counterparties.

Abstract

We investigate the efficiency and stability of R&D networks in a model with network-dependent indirect spillovers. We show that the efficient network structure critically depends on the marginal cost of R&D collaborations. When the marginal cost is low, the complete graph is efficient, while high marginal costs imply that the efficient network is asymmetric and has a nested structure. Regarding the stability of network structures, we show the existence of both symmetric and asymmetric equilibria. The efficient network is stable for small industry size and small cost. In contrast, for large industry size, there is a wide region of cost in which the efficient network is not stable. This implies a divergence between efficiency and stability in large industries.

Abstract

The increasing diversity of consumers’ demand, as documented by the debate on the long tail of the distribution of sales volume across products, represents a challenge for retail stores. Recommender systems offer a tool to cope with this challenge. The recent developments in information technology and ubiquitous computing makes it feasible to move recommender systems from the on-line commerce, where they are widely used, to retail stores. In this paper, we aim to bridge the management literature and the computer science literature by analysing a number of issues that arise when applying recommender systems to retail stores: these range from the format of the stores that would benefit most from recommender systems to the impact of coverage and control of recommender systems on customer loyalty and competition among retail stores.

Abstract

In this paper, we investigate the network of ownership relationships among European firms and its embedding in the geographical space.We carry out a detailed analysis of geographical distances between pairs of nodes, connected by edges or by shortest paths of varying length. In particular, we study the relation between geographical distance and network distance in comparison with a random spatial network model. While the distribution of geographical distance can be fairly well reproduced, important deviations appear in the network distance and in the size of the largest strongly connected component. Our results show that geographical factors allow us to capture several features of the network, while the deviations quantify the effect of additional economic factors at work in shaping the topology. The analysis is relevant to other types of geographically embedded networks and sheds light on the link formation process in the presence of spatial constraints.

Abstract

The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic ‘‘super-entity’’ that raises new important issues both for researchers and policy makers.

Abstract

We introduce a new model for the evolution of networks of firms exchanging knowledge in R&D partnerships. Innovation is assumed to result from the recombination of knowledge among firms in an R&D intensive industry. The decision of two firms to establish a new partnerships or to terminate an existing one, is based on their marginal revenues and costs, which in turn depend on the position they occupy in the network. Moreover, the formation of a collaboration has significant external effects on the other firms in the same connected component of the network. We show that this decentralized partner selection process leads to the existence of multiple equilibrium structures. Finally, by means of computer simulations, we study the properties of the emerging equilibrium networks and we show that they reproduce the stylized facts of R&D networks.

Abstract

We propose a novel trust metric for social networks which is suitable for application in recommender systems. It is personalised and dynamic and allows to compute the indirect trust between two agents which are not neighbours based on the direct trust between agents that are neighbours. In analogy to some personalised versions of PageRank, this metric makes use of the concept of feedback centrality and overcomes some of the limitations of other trust metrics.In particular, it does not neglect cycles and other patterns characterising social networks, as some other algorithms do. In order to apply the metric to recommender systems, we propose a way to make trust dynamic over time. We show by means of analytical approximations and computer simulations that the metric has the desired properties. Finally, we carry out an empirical validation on a dataset crawled from an Internet community and compare the performance of a recommender system using our metric to one using collaborative filtering.

Abstract

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∗,and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of X∗ 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 leads to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions determine a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.

Abstract

We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge production, firms follow different strategies to create and/or to delete links with other firms. Dependent on the information firms take into account for their decision, we find the emergence of different network structures. We analyze the conditions for the existence of these structures within a mathematical approach and underpin our findings by extensive computer simulations which show the evolution of the networks and their equilibrium state. In the discussion of the results, particular attention is given to the emergence of direct and indirect reciprocity in knowledge exchange, which refers to the emergence of cycles in the network structure. In order to motivate our modeling framework, in the first part of the chapter we give a broad overview of existing literature from economics and physics. This shows that our framework bridges and extends two different lines of research, namely the study of equilibrium networks with simple topologies and the dynamic approach of hypercycle models.

Abstract

We present a methodology to extract the backbone of complex networks based on the weight and direction of links, as well as on nontopological properties of nodes. We show how the methodology can be applied in general to networks in which mass or energy is flowing along the links. In particular, the procedure enables us to address important questions in economics, namely, how control and wealth are structured and concentrated across national markets.We report on the first cross-country investigation of ownership networks, focusing on the stock markets of 48 countries around the world. On the one hand, our analysis confirms results expected on the basis of the literature on corporate control, namely, that in Anglo-Saxon countries control tends to be dispersed among numerous shareholders. On the other hand, it also reveals that in the same countries, control is found to be highly concentrated at the global level, namely, lying in the hands of very few important shareholders. Interestingly, the exact opposite is observed for European countries. These results have previ-ously not been reported as they are not observable without the kind of network analysis developed here

Abstract

The 20 research articles collected in this issue share, in addition to their topical relations, one important feature: they present results obtained from research groups associated in the COST action P10 ‘Physics of Risk’. COST is an intergovernmental framework for ‘European Cooperation in Science and Technology’, allowing the coordination of research on a European level. The action P10 was funded between September 2003 and June 2008 and involved more than 80 scientists in 21 countries across Europe. The main objective of the action was to apply methods developed in statistical physics to accomplish a new quantitative understanding of the assessment of risk. This way it departed from usual activities in the field of risk management. In fact, in recent years statistical physics has successfully contributed to many interdisciplinary fields ranging from regulatory networks in biology to financial market models. Therefore, a transfer of methods and tools from statistical physics into the area of risk assessment should be a promising endeavour.

Abstract

Networks play an important role in a wide range of economic phenomena. Despite this fact, standard economic theory rarely considers economic networks explicitly in its analysis. However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. This recent development has lead to a fast increase in theoretical research on economic networks. In this tutorial, we introduce the reader to some basic concepts used in a wide range of models of economic networks.

Abstract

In this chapter, we present a model recently introduced in [14, 16] and we discuss the features of a networked economy in which N firms are organised in M production levels. Each firm at a certain level is supplied by a subset of firms in the upper level (suppliers) and supplies a subset of the firms in the lower level (customers). The bottom level consists of retailers, i.e., firms that sell in the consumer market. The top level consists of firms that provide primary goods to the other firms. Firms are connected by means of two mech-anisms: (i) the output of supplier firms is an input for customer firms; (ii) supplier firms extend trade credit to customers (as it is typically the case in reality). However, in the model, the trade credit contract is only implicitly sketched: we neither design the optimal trade credit scheme nor look for the optimal amount of trade credit a customer firm should require. Instead, we focus on the mechanisms of propagation of bankruptcy .

Abstract

Over the recent decade, the Internet has conquered people’s homes and life: they pursue an increasing amount of activities on the World Wide Web and this has fundamentally impacted the lifestyle of society. For example, people use their computers for communication with others, to buy and sell products on-line, to search for information, and to carry out many more tasks. Along this development, so far unknown ways of marketing, trading and information sharing are booming. This situation is made possible by a set of related emerging technologies centred around the Internet – just to mention a few: collaborative work and information sharing environments, peer-to-peer networks, and rating, recommendation, and reputation systems. At the economic level, the impact of these technologies is already very high and it is expected to grow even more in the future. The Internet has become a social network, “linking people, organisations, and knowledge” [2] and it has taken the role of a platform on which people pursue an increasing amount of tasks that they have usually only done in the real-world. An approach looking at these emerging technologies and their effects from a complex systems perspective can, as wewill show in this chapter, be very useful.

Abstract

This work introduces a new model to investigate the efficiency and evolution of networks of firms exchanging knowledge in R&D partnerships. We first examine the efficiency of a given network structure in terms of the maximization of total profits in the industry. We show that the efficient network structure depends on the marginal cost of collaboration. When the marginal cost is low, the complete graph is efficient. However, a high marginal cost implies that the efficient network is sparser and has a core-periphery structure. Next, we examine the evolution of the network structure when the decision on collaborating partners is decentralized. We show the existence of multiple equilibrium structures which are in general inefficient. This is due to (i) the path dependent character of the partner selection process, (ii) the presence of knowledge externalities and (iii) the presence of severance costs involved in link deletion. Finally, we study the properties of the emerging equilibrium networks and we show that they are coherent with the stylized facts of R&D networks.

Abstract

We investigate some of the properties and extensions of a dynamic innovation network model recently introduced in $$citep07:_effic_stabil_dynam_innov_networ. In the model, the set of efficient graphs ranges, depending on the cost for maintaining a link, from the complete graph to the (quasi-) star, varying within a well defined class of graphs. However, the interplay between dynamics on the nodes and topology of the network leads to equilibrium networks which are typically not efficient and are characterized, as observed in empirical studies of R&D networks, by sparseness, presence of clusters and heterogeneity of degree. In this paper, we analyze the relation between the growth rate of the knowledge stock of the agents from R&D collaborations and the properties of the adjacency matrix associated with the network of collaborations. By means of computer simulations we further investigate how the equilibrium network is affected by increasing the evaluation time $ tau$ over which agents evaluate whether to maintain a link or not. We show that only if $ tau$ is long enough, efficient networks can be obtained by the selfish link formation process of agents, otherwise the equilibrium network is inefficient. This work should assist in building a theoretical framework of R&D networks from which policies can be derived that aim at fostering efficient innovation networks.

Abstract

We study the mean field approximation of a recent model of cascades on networks relevant to the investigation of systemic risk control in financial networks. In the model, the hypothesis of a trend reinforcement in the stochastic process describing the fragility of the nodes, induces a trade-off in the systemic risk with respect to the density of the network. Increasing the average link density, the network is first less exposed to systemic risk, while above an intermediate value the systemic risk increases. This result offers a simple explanation for the emergence of instabilities in financial systems that get increasingly interwoven. In this paper, we study the dynamics of the probability density function of the average fragility. This converges to a unique stable distribution which can be computed numerically and can be used to estimate the systemic risk as a function of the parameters of the model.

Abstract

In this paper, we present a model of a trust-based recommendation system on a social network. The idea of the model is that agents use their social network to reach information and their trust relationships to filter it. We investigate how the dynamics of trust among agents affect the performance of the system by comparing it to a frequency-based recommendation system. Furthermore, we identify the impact of network density, preference heterogeneity among agents, and knowledge sparseness to be crucial factors for the performance of the system. The system self-organises in a state with performance near to the optimum; the performance on the global level is an emergent property of the system, achieved without explicit coordination from the local interactions of agents.

Abstract

We propose a methodological framework to study the dynamics of inter-regional investment flow in Europe from a Complex Networks perspective, an approach with recent proven success in many fields including economics. In this work we study the network of investment stocks in Europe at two different levels: first, we compute the inward-outward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inward-outward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. Despite the intuitive value of this approach for EU policy making in economic development, to our knowledge there are no similar works in the literature yet. In this paper we focus on statistical distributions and scaling laws of activity, investment stock and connectivity degree both at the level of firms and at the level of regions. In particular we find that investment stock of firms is power law distributed with an exponent very close to the one found for firm activity. On the other hand investment stock and activity of regions turn out to be log-normal distributed. At both levels we find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales with connectivity in a similar way as has been previously found for stock market data, calling for further investigations on a possible general scaling law holding true in economical networks.

Abstract

We present a simple model of a production network in which firms are linked by supplier–customer relationships involving extension of trade–credit. Our aim is to identify the minimal set of mechanisms which reproduce qualitatively the main stylized facts of industrial demography, such as firms’ size distribution, and, at the same time, the correlation, over time and across firms, of output, growth and bankruptcies. The behavior of aggregate variables can be traced back to the direct firm–firm interdependence. In this paper, we assume that the number of firms is constant and the network has a periodic static structure. But the framework allows further extensions to investigate which network structures are more robust against domino effects and, if the network is let to evolve in time, which structures emerge spontaneously, depending on the individual strategies for orders and delivery.

Abstract

We investigate the dynamics of the creation, development, and breakup of social networks formed by coalitions of agents. As an application, we consider coalition formation in a consumer electronic market. In our model, agents have benefits and costs from establishing a social network by participating in a coalition. Buyers benefit in terms of volume discount and better match of their preferences. Sellers benefit in terms of better predictability of sales volumes. The model allows us to investigate the stability and size of the coalitions as well as the performance of the market in terms of utility of the agents. We find that the system exhibits three different dominating regimes: individual purchasing behaviour, i.e., no social network exists among the agents, formation of several heterogenous coalitions, i.e., a number of social networks which are not connected, as well as condensation to a giant coalition, i.e., a social network involving all agents.

Abstract

Although standard economics textbooks are seldom interested in production networks, modern economies are more and more based upon supplier/customer interactions.Onecan consider entire sectors of theeconomy as generalised supply chains.We will take this view in the present paper and study under which conditions local failures to produce or simply to deliver can result in avalanches of shortage and bankruptcies and in localisation of the economic activity.We will showthat a large class of models exhibit scale free distributions of production and wealth among firms and that regions of high production are localised.

Abstract

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree (kin) and the sum of incoming link weights (v) of an investor correspond to the number of assets held (portfolio diversification) and to the invested wealth (portfolio volume), respectively. An empirical analysis of three different real markets reveals that the distributions of both kin and v display power-law tails with exponents g and a: Moreover, we find that kin scales as a power-law function of v with an exponent b: Remarkably, despite the values of a; b and g differ across the three markets, they are always governed by the scaling relation b ¼ð1aÞ = ð1gÞ: We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of ‘hidden’ vertex properties.