Triadic motifs and dyadic self-organization in the World Trade Network

In self-organizing networks, topology and dynamics coevolve in a continuous feedback, without exogenous driving. The World Trade Network (WTN) is one of the few empirically well documented examples of self-organizing networks: its topology strongly depends on the GDP of world countries, which in turn depends on the structure of trade. Therefore, understanding which are the key topological properties of the WTN that deviate from randomness provides direct empirical information about the structural effects of self-organization. Here, using an analytical pattern-detection method that we have recently proposed, we study the occurrence of triadic "motifs" (subgraphs of three vertices) in the WTN between 1950 and 2000. We find that, unlike other properties, motifs are not explained by only the in- and out-degree sequences. By contrast, they are completely explained if also the numbers of reciprocal edges are taken into account. This implies that the self-organization process underlying the evolution of the WTN is almost completely encoded into the dyadic structure, which strongly depends on reciprocity.Comment: 12 pages, 3 figures; Best Paper Award at the 6th International Conference on Self-Organizing Systems, Delft, The Netherlands, 15-16/03/201

Structure and Evolution of the World Trade Network

The \emph{World Trade Web} (WTW), the network defined by the international import/export trade relationships, has been recently shown to display some important topological properties which are tightly related to the Gross Domestic Product of world countries. While our previous analysis focused on the static, undirected version of the WTW, here we address its full evolving, directed description. This is accomplished by exploiting the peculiar reciprocity structure of the WTW to recover the directed nature of international trade channels, and by studying the temporal dependence of the parameters describing the WTW topology.Comment: Proceedings of the "First Bonzenfreies Colloquium on Market Dynamics and Quantitative Economics", Alessandria (ITALY) September 9-10, 2004. One of the three awarded talk

Experimental evidence for the interplay between individual wealth and transaction network

We conduct a market experiment with human agents in order to explore the structure of transaction networks and to study the dynamics of wealth accumulation. The experiment is carried out on our platform for 97 days with 2,095 effective participants and 16,936 times of transactions. From these data, the hybrid distribution (log-normal bulk and power-law tail) in the wealth is observed and we demonstrate that the transaction networks in our market are always scale-free and disassortative even for those with the size of the order of few hundred. We further discover that the individual wealth is correlated with its degree by a power-law function which allows us to relate the exponent of the transaction network degree distribution to the Pareto index in wealth distribution.Comment: 6 pages, 7 figure

Interplay between topology and dynamics in the World Trade Web

We present an empirical analysis of the network formed by the trade relationships between all world countries, or World Trade Web (WTW). Each (directed) link is weighted by the amount of wealth flowing between two countries, and each country is characterized by the value of its Gross Domestic Product (GDP). By analysing a set of year-by-year data covering the time interval 1950-2000, we show that the dynamics of all GDP values and the evolution of the WTW (trade flow and topology) are tightly coupled. The probability that two countries are connected depends on their GDP values, supporting recent theoretical models relating network topology to the presence of a `hidden' variable (or fitness). On the other hand, the topology is shown to determine the GDP values due to the exchange between countries. This leads us to a new framework where the fitness value is a dynamical variable determining, and at the same time depending on, network topology in a continuous feedback.Comment: Proceedings of the 5th conference on Applications of Physics in Financial Analysis (APFA5), 29 June - 1 July 2006, Torino (ITALY

The scale-free topology of market investments

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 ($k_{in}$) and the sum of incoming link weights ($v$) of an investor correspond to the number of assets held (\emph{portfolio diversification}) and to the invested wealth (\emph{portfolio volume}) respectively. An empirical analysis of three different real markets reveals that the distributions of both $k_{in}$ and $v$ display power-law tails with exponents $\gamma$ and $\alpha$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $\beta$. Remarkably, despite the values of $\alpha$, $\beta$ and $\gamma$ differ across the three markets, they are always governed by the scaling relation $\beta=(1-\alpha)/(1-\gamma)$. 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.Comment: Final version accepted for publication on Physica

Uncovering the mesoscale structure of the credit default swap market to improve portfolio risk modelling

One of the most challenging aspects in the analysis and modelling of financial markets, including Credit Default Swap (CDS) markets, is the presence of an emergent, intermediate level of structure standing in between the microscopic dynamics of individual financial entities and the macroscopic dynamics of the market as a whole. This elusive, mesoscopic level of organisation is often sought for via factor models that ultimately decompose the market according to geographic regions and economic industries. However, at a more general level the presence of mesoscopic structure might be revealed in an entirely data-driven approach, looking for a modular and possibly hierarchical organisation of the empirical correlation matrix between financial time series. The crucial ingredient in such an approach is the definition of an appropriate null model for the correlation matrix. Recent research showed that community detection techniques developed for networks become intrinsically biased when applied to correlation matrices. For this reason, a method based on Random Matrix Theory has been developed, which identifies the optimal hierarchical decomposition of the system into internally correlated and mutually anti-correlated communities. Building upon this technique, here we resolve the mesoscopic structure of the CDS market and identify groups of issuers that cannot be traced back to standard industry/region taxonomies, thereby being inaccessible to standard factor models. We use this decomposition to introduce a novel default risk model that is shown to outperform more traditional alternatives.Comment: Quantitative Finance (2021