Market structure explained by pairwise interactions

We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing FSE were found. First transition is from a hierarchical scale-free MST representing the stock market...

The credit crisis roiling the world's financial markets will likely take years and entire careers to fully understand and analyze. A short empirical investigation of the current trends, however, demonstrates that the losses in certain markets, in this case the US equity markets, follow a cascade or epidemic flow like model along the correlations of various stocks. This phenomenon will be shown by the graphical display of stock returns across the network as well as the depende...

Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during trend reversals dominated by the pairwise component. In particular, these events are predicted with high significant accuracy by the ensemble's instantaneous state...

Summarized by the efficient market hypothesis, the idea that stock prices fully reflect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efficiency of stock markets, most studies assume this efficiency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we define the time-varying efficiency of stock markets by calculating the...

The understanding of complex systems has become a central issue because complex systems exist in a wide range of scientific disciplines. Time series are typical experimental results we have about complex systems. In the analysis of such time series, stationary situations have been extensively studied and correlations have been found to be a very powerful tool. Yet most natural processes are non-stationary. In particular, in times of crisis, accident or trouble, stationarity i...

We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing the stable state of WSE before the recent worldwide financial crash, to a superstar-like (or superhub) MST network of the market decorated by a hierarchy of trees (being, perhaps, an unstable, intermediate market state). Subsequently, we obs...

Over the last two decades, financial systems have been studied and analysed from the perspective of complex networks, where the nodes and edges in the network represent the various financial components and the strengths of correlations between them. Here, we adopt a similar network-based approach to analyse the daily closing prices of 69 global financial market indices across 65 countries over a period of 2000-2014. We study the correlations among the indices by constructing ...

This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets' dependencies, especially correlational studies, which in our opinion are beneficial for researchers in both fields. In econophysics, these dependencies can be modeled to describe financial markets as evolving complex networks. In particular we show that a useful way t...

With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the sector mode, the average correlation inside the sectors is positive, while that between the sectors is negative. Further, we explore the time evolution of the intera...

In this paper we study Algorithmic High-Frequency Financial Markets as dynamical networks. After an individual analysis of 24 stocks of the US market during a trading year of fully automated transactions by means of ordinal pattern series, we define an information-theoretic measure of pairwise synchronization for time series which allows us to study this subset of the US market as a dynamical network. We apply to the resulting network a couple of clustering algorithms in orde...