Causal Hierarchy in the Financial Market Network-Uncovered by the Helmholtz-Hodge-Kodaira Decomposition.

Granger causality can uncover the cause-and-effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into rotational and gradient components which reveal the hierarchy of the Granger causality flow. Using Kenneth French's business sector return time series, it is revealed that during the COVID crisis, precious metals and pharmaceutical products were causal drivers of the financial network. Moreover, the estimated Granger causality network shows a high connectivity during the crisis, which means that the research presented here can be especially useful for understanding crises in the market better by revealing the dominant drivers of crisis dynamics.

Cooperation in a non-ergodic world on a network - insurance and beyond.

Cooperation between individuals is emergent in all parts of society; yet, mechanistic reasons for this emergence are ill understood in the literature. A specific example of this is insurance. Recent work has, though, shown that assuming the risk individuals face is proportional to their wealth and optimizing the time average growth rate rather than the ensemble average results in a non-zero-sum game, where both parties benefit from cooperation through insurance contracts. In a recent paper, Peters and Skjold present a simple agent-based model and show how, over time, agents that enter into such cooperatives outperform agents that do not. Here, we extend this work by restricting the possible connections between agents via a lattice network. Under these restrictions, we still find that all agents profit from cooperating through insurance. We, though, further find that clusters of poor and rich agents emerge endogenously on the two-dimensional map and that wealth inequalities persist for a long duration, consistent with the phenomenon known as the poverty trap. By tuning the parameters that control the risk levels, we simulate both highly advantageous and extremely risky gambles and show that despite the qualitative shift in the type of risk, the findings are consistent.

Estimating stable fixed points and Langevin potentials for financial dynamics.

The geometric Brownian motion (GBM) is a standard model in quantitative finance, but the potential function of its stochastic differential equation (SDE) cannot include stable nonzero prices. This article generalizes the GBM to an SDE with polynomial drift of order q and shows via model selection that q=2 is most frequently the optimal model to describe the data. Moreover, Markov chain Monte Carlo ensembles of the accompanying potential functions show a clear and pronounced potential well, indicating the existence of a stable price.

The characteristic time scale of cultural evolution.

Numerous researchers from various disciplines have explored commonalities and divergences in the evolution of complex social formations. Here, we explore whether there is a "characteristic" time course for the evolution of social complexity in a handful of different geographic areas. Data from the Seshat: Global History Databank is shifted so that the overlapping time series can be fitted to a single logistic regression model for all 23 geographic areas under consideration. The resulting regression shows convincing out-of-sample predictions, and its period of extensive growth in social complexity can be identified via bootstrapping as a time interval of roughly 2,500 years. To analyze the endogenous growth of social complexity, each time series is restricted to a central time interval without major disruptions in cultural or institutional continuity, and both approaches result in a similar logistic regression curve. Our results suggest that these different areas have indeed experienced a similar course in the their evolution of social complexity, but that this is a lengthy process involving both internal developments and external influences.

Memory Effects, Multiple Time Scales and Local Stability in Langevin Models of the S&P500 Market Correlation.

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500, which corresponds to the main market mode in principle component analysis. We fit a generalised Langevin equation (GLE) to the data whose memory kernel implies that there is a significant memory effect in the market correlation ranging back at least three trading weeks. The memory kernel improves the forecasting accuracy of the GLE compared to models without memory and hence, such a memory effect has to be taken into account for optimal portfolio selection to minimise risk or for predicting future correlations. Moreover, a Bayesian resilience estimation provides further evidence for non-Markovianity in the data and suggests the existence of a hidden slow time scale that operates on much slower times than the observed daily market data. Assuming that such a slow time scale exists, our work supports previous research on the existence of locally stable market states.

Efficient Multi-Change Point Analysis to Decode Economic Crisis Information from the S&P500 Mean Market Correlation.

Identifying macroeconomic events that are responsible for dramatic changes of economy is of particular relevance to understanding the overall economic dynamics. We introduce an open-source available efficient Python implementation of a Bayesian multi-trend change point analysis, which solves significant memory and computing time limitations to extract crisis information from a correlation metric. Therefore, we focus on the recently investigated S&P500 mean market correlation in a period of roughly 20 years that includes the dot-com bubble, the global financial crisis, and the Euro crisis. The analysis is performed two-fold: first, in retrospect on the whole dataset and second, in an online adaptive manner in pre-crisis segments. The online sensitivity horizon is roughly determined to be 80 up to 100 trading days after a crisis onset. A detailed comparison to global economic events supports the interpretation of the mean market correlation as an informative macroeconomic measure by a rather good agreement of change point distributions and major crisis events. Furthermore, the results hint at the importance of the U.S. housing bubble as a trigger of the global financial crisis, provide new evidence for the general reasoning of locally (meta)stable economic states, and could work as a comparative impact rating of specific economic events.

Analysis of the Football Transfer Market Network.

Using publicly available data from the football database transfermarkt.co.uk, it is possible to construct a trade network between football clubs. This work regards the network of the flow of transfer fees between European top league clubs from eight countries between 1992 and 2020 to analyse the network of each year's transfer market. With the transfer fees as weights, the market can be represented as a weighted network in addition to the classic binary network approach. This opens up the possibility to study various topological quantities of the network, such as the degree and disparity distributions, the small-world property and different clustering measures. This article shows that these quantities stayed rather constant during the almost three decades of transfer market activity, even despite massive changes in the overall market volume.