Paolo Barucca

Disentangling bipartite and core-periphery structure in financial networks

A growing number of systems are represented as networks whose architecture conveys significant information and determines many of their properties. Examples of network architecture include modular, bipartite, and core-periphery structures. However inferring the network structure is a non trivial task and can depend sometimes on the chosen null model. Here we propose a method for classifying network structures and ranking its nodes in a statistically well-grounded fashion. The method is based on the use of Belief Propagation for learning through Entropy Maximization on both the Stochastic Block Model (SBM) and the degree-corrected Stochastic Block Model (dcSBM). As a specific application we show how the combined use of the two ensembles -SBM and dcSBM- allows to disentangle the bipartite and the core-periphery structure in the case of the e-MID interbank network. Specifically we find that, taking into account the degree, this interbank network is better described by a bipartite structure, while using the SBM the core-periphery structure emerges only when data are aggregated for more than a week.

Network Valuation in Financial Systems

We introduce a network valuation model (hereafter NEVA) for the ex-ante valuation of claims among financial institutions connected in a network of liabilities. Similar to previous work, the new framework allows to endogenously determine the recovery rate on all claims upon the default of some institutions. In addition, it also allows to account for ex-ante uncertainty on the asset values, in particular the one arising when the valuation is carried out at some time before the maturity of the claims. The framework encompasses as special cases both the ex-post approaches of Eisenberg and Noe and its previous extensions, as well as the ex-ante approaches, in the sense that each of these models can be recovered exactly for special values of the parameters. We characterize the existence and uniqueness of the solutions of the valuation problem under general conditions on how the value of each claim depends on the equity of the counterparty. Further, we define an algorithm to carry out the network valuation and we provide sufficient conditions for convergence to the maximal solution.

The organization of the interbank network and how ECB unconventional measures affected the e-MID overnight market

The topological properties of interbank networks have been discussed widely in the literature mainly because of their relevance for systemic risk. Here we propose to use the Stochastic Block Model to investigate and perform a model selection among several possible two block organizations of the network: these include bipartite, core-periphery, and modular structures. We apply our method to the e-MID interbank market in the period 2010–2014 and we show that in normal conditions the most likely network organization is a bipartite structure. In exceptional conditions, such as after LTRO, one of the most important unconventional measures by ECB at the beginning of 2012, the most likely structure becomes a random one and only in 2014 the e-MID market went back to a normal bipartite organization. By investigating the strategy of individual banks, we explore possible explanations and we show that the disappearance of many lending banks and the strategy switch of a very small set of banks from borrower to lender is likely at the origin of this structural change.

Centrality metrics and localization in core-periphery networks

Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it have been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The second is related to large scale organization of the network, the core-periphery structure, composed by a dense core plus an outlying and loosely-connected periphery. In this paper we investigate the relation between these two concepts. We consider networks generated via the stochastic block model, or its degree corrected version, with a core-periphery structure and we investigate the centrality properties of the core nodes and the ability of several centrality metrics to identify them. We find that the three measures with the best performance are marginals obtained with belief propagation, PageRank, and degree centrality, while non-backtracking and eigenvector centrality (or MINRES [10], showed to be equivalent to the latter in the large network limit) perform worse in the investigated networks.

Network models of financial systemic risk: A review

The global financial system can be represented as a large complex network in which banks, hedge funds and other financial institutions are interconnected to each other through visible and invisible financial linkages. Recently, a lot of attention has been paid to the understanding of the mechanisms that can lead to a breakdown of this network. This can happen when the existing financial links turn from being a means of risk diversification to channels for the propagation of risk across financial institutions. In this review article, we summarize recent developments in the modeling of financial systemic risk. We focus, in particular, on network approaches, such as models of default cascades due to bilateral exposures or to overlapping portfolios, and we also report on recent findings on the empirical structure of interbank networks. The current review provides a landscape of the newly arising interdisciplinary field lying at the intersection of several disciplines, such as network science, physics, engineering, economics, and ecology.

Resolution of ranking hierarchies in directed networks

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.

Tackling Information Asymmetry in Networks: A New Entropy-Based Ranking Index

Information is a valuable asset in socio-economic systems, a significant part of which is entailed into the network of connections between agents. The different interlinkages patterns that agents establish may, in fact, lead to asymmetries in the knowledge of the network structure; since this entails a different ability of quantifying relevant, systemic properties (e.g. the risk of contagion in a network of liabilities), agents capable of providing a better estimation of (otherwise) inaccessible network properties, ultimately have a competitive advantage. In this paper, we address the issue of quantifying the information asymmetry of nodes: to this aim, we define a novel index—InfoRank—intended to rank nodes according to their information content. In order to do so, each node ego-network is enforced as a constraint of an entropy-maximization problem and the subsequent uncertainty reduction is used to quantify the node-specific accessible information. We, then, test the performance of our ranking procedure in terms of reconstruction accuracy and show that it outperforms other centrality measures in identifying the “most informative” nodes. Finally, we discuss the socio-economic implications of network information asymmetry.

Network Models of Financial Systemic Risk: A Review

The global financial system can be represented as a large complex network in which banks, hedge funds and other financial institutions are interconnected to each other through visible and invisible financial linkages. Recently, a lot of attention has been paid to the understanding of the mechanisms that can lead to a breakdown of this network. This can happen when the existing financial links turn from being a means of risk diversification to channels for the propagation of risk across financial institutions. In this review article, we summarize recent developments in the modeling of financial systemic risk. We focus in particular on network approaches, such as models of default cascades due to bilateral exposures or to overlapping portfolios, and we also report on recent findings on the empirical structure of interbank networks. The current review provides a landscape of the newly arising interdisciplinary field lying at the intersection of several disciplines, such as network science, physics, engineering, economics, and ecology.

Behind the Price: On the Role of Agent’s Reflexivity in Financial Market Microstructure

In this chapter we review some recent results on the dynamics of price formation in financial markets and its relations with the efficient market hypothesis. Specifically, we present the limit order book mechanism for markets and we introduce the concepts of market impact and order flow, presenting their recently discovered empirical properties and discussing some possible interpretation in terms of agent’s strategies. Our analysis confirms that quantitative analysis of data is crucial to validate qualitative hypothesis on investors’ behavior in the regulated environment of order placement and to connect these micro-structural behaviors to the properties of the collective dynamics of the system as a whole, such for instance market efficiency. Finally we discuss the relation between some of the described properties and the theory of reflexivity proposing that in the process of price formation positive and negative feedback loops between the cognitive and manipulative function of agents are present.