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arXiv2010

How to grow a bubble: A model of myopic adapting agents

We present a simple agent-based model to study the development of a bubble and the consequential crash and investigate how their proximate triggering factor might relate to their fundamental mechanism, and vice versa. Our agents invest according to their opinion on future price movements, which is based on three sources of information, (i) public information, i.e. news, (ii) information from their "friendship" network and (iii) private information. Our bounded rational agents continuously adapt their trading strategy to the current market regime by weighting each of these sources of information in their trading decision according to its recent predicting performance. We find that bubbles originate from a random lucky streak of positive news, which, due to a feedback mechanism of these news on the agents' strategies develop into a transient collective herding regime. After this self-amplified exuberance, the price has reached an unsustainable high value, being corrected by a crash, which brings the price even below its fundamental value. These ingredients provide a simple mechanism for the excess volatility documented in financial markets. Paradoxically, it is the attempt for investors to adapt to the current market regime which leads to a dramatic amplification of the price volatility. A positive feedback loop is created by the two dominating mechanisms (adaptation and imitation) which, by reinforcing each other, result in bubbles and crashes. The model offers a simple reconciliation of the two opposite (herding versus fundamental) proposals for the origin of crashes within a single framework and justifies the existence of two populations in the distribution of returns, exemplifying the concept that crashes are qualitatively different from the rest of the price moves.

q-fin.TR↗
arXiv2008

The Question of Relaxation in the Wealth Exchange Models

We look at the meaning of 'relaxation' in the wealth exchange models that are recently proposed in Econophysics to interpret the wealth distributions. To quantify and characterise the process of relaxation, we define an appropriate quantity and evaluate that numerically for the systems of many agents. Also, the numerical results have been supported heuristically by constructing a simple differential equation.

q-fin.GN↗
arXiv2008

Established Clustering Procedures for Network Analysis

In light of the burgeoning interest in network analysis in the new millenium, we bring to the attention of contemporary network theorists, a two-stage double-standarization and hierarchical clustering (single-linkage-like) procedure devised in 1974. In its many applications over the next decade--primarily to the migration flows between geographic subdivisions within nations--the presence was often revealed of ``hubs''. These are, typically, ``cosmopolitan/non-provincial'' areas--such as the French capital, Paris--which send and receive people relatively broadly across their respective nations. Additionally, this two-stage procedure--which ``might very well be the most successful application of cluster analysis'' (R. C. Dubes)--has detected many (physically or socially) isolated groups (regions) of areas, such as those forming the southern islands, Shikoku and Kyushu, of Japan, the Italian islands of Sardinia and Sicily, and the New England region of the United States. Further, we discuss a (complementary) approach developed in 1976, involving the application of the max-flow/min-cut theorem to raw/non-standardized flows.

physics.soc-ph↗
arXiv2009

Descent curve and the phases of collapse of WTC 7

We examine four WTC 7 descent curves, labeled "C," "E," "N," and "O," either anonymously published, or confidentially communicated to us. Descent curve describes apparent height of a collapsing building as a function of time. The set "C" suggests that there are three active phases of collapse. Phase I is a free fall for the first $H_1\simeq28$m or $T_1\simeq2.3$s, during which the acceleration $a$ is that of the gravity, $a=g=9.8$m/s$^2$. In Phase II, which continues until drop $H_2\simeq68$m, or $T_2\simeq3.8$s, the acceleration is $a\simeq5$m/s$^2$, while in Phase III which continues for the remaining of the data set, $a \simeq -1$m/s$^2$. We propose that the collapse of WTC 7 is initiated by a total and sudden annihilation of the base (section of the building from the ground level to $H_1$), which then allows the top section (building above $H_1$) to free fall during Phase I, and then collide with the ground in Phase II and III. The total duration of the collapse, assuming that Phase III continues to the end, is in the range $7.8-8.6$s. We derive a physical model for collision of the building with the ground, in which we correct the "crush-up" model of Bažant and Verdure, J. Engr. Mech. ASCE, {\bf 133} (2006) 308, and estimate the magnitude of the resistive force in the top section. We compare our findings to those of NIST investigators and find an agreement with respect to the distribution of damage in the primary zone. We conclude that the building was destroyed in a highly controlled fashion.

physics.pop-ph↗
arXiv2008

Discernment of Hubs and Clusters in Socioeconomic Networks

Interest in the analysis of networks has grown rapidly in the new millennium. Consequently, we promote renewed attention to a certain methodological approach introduced in 1974. Over the succeeding decade, this two-stage--double-standardization and hierarchical clustering (single-linkage-like)--procedure was applied to a wide variety of weighted, directed networks of a socioeconomic nature, frequently revealing the presence of ``hubs''. These were, typically--in the numerous instances studied of migration flows between geographic subdivisions within nations--``cosmopolitan/non-provincial'' areas, a prototypical example being the French capital, Paris. Such locations emit and absorb people broadly across their respective nations. Additionally, the two-stage procedure--which ``might very well be the most successful application of cluster analysis'' (R. C. Dubes, 1985)--detected many (physically or socially) isolated, functional groups (regions) of areas, such as the southern islands, Shikoku and Kyushu, of Japan, the Italian islands of Sardinia and Sicily, and the New England region of the United States. Further, we discuss a (complementary) approach developed in 1976, in which the max-flow/min-cut theorem was applied to raw/non-standardized (interindustry, as well as migration) flows.

physics.soc-ph↗
arXiv2008

Global recessions as a cascade phenomenon with heterogenous, interacting agents

I examine global recessions as a cascade phenomenon. In other words, how recessions arising in one or more countries might percolate across a network of connected economies. A heterogeneous agent based model is set up in which the agents are Western economies. A country has a probability of entering a recession in any given year and one of emerging from it the next. In addition, the agents have a unique threshold propensity to import a recession from the agents with which they have the strongest connections. They are connected on a small world topology, and an agent's neighbours at any time are either in (state 1) or out (state 0) of recession. If the weighted sum exceeds the threshold, the agent goes into recession. Annual real GDP growth for 17 Western countries 1871-2006 is used as the data set. The distribution of the number of countries in recession in any given year is exponential, as is the duration of recessions within individual countries. The model is calibrated against these two facts, plus the 'wait time' between recessions. It is able to replicate them successfully. The network structure is essential for the agents to replicate the stylised facts. The country-specific probabilities of entering and emerging from recession by themselves give results very different to the actual data.

q-fin.GN↗
arXiv2008

Random matrix theory and the evolution of business cycle synchronisation 1886-2006

The major study by Bordo and Helbing (2003) analyses the business cycle in Western economies 1881-2001. They examine four distinct periods in economic history, and conclude that there is a secular trend towards greater synchronisation for much of the 20th century. Their analysis, in common with the standard economic literature on business cycle synchronisation, relies upon the estimation of an empirical correlation matrix of time series data of macroeconomic aggregates. However because of the small number of observations and economies, the empirical correlation matrix may contain considerable noise. Random matrix theory was developed to overcome this problem. I use random matrix theory, and the associated technique of agglomerative hierarchical clustering, to examine the evolution of business cycle synchronisation between the capitalist economies in the long-run. Contrary to the findings of Bordo and Helbing, it is not possible to speak of a 'secular trend' towards greater synchronisation over the period as a whole. During the pre-First World War period, the cross-country correlations of annual real GDP growth are indistinguishable from those which could be generated by a purely random matrix. The periods 1920-38 and 1948-72 do show a certain degree of synchronisation, but it is very weak. In particular, the cycles of the major economies cannot be said to be synchronised. Such synchronisation as exists in the overall data is due to meaningful co-movements in sub-groups. So the degree of synchronisation has evolved fitfully. It is only in the most recent 1973-2006 period that we can speak meaningfully of anything resembling an international business cycle.

q-fin.ST↗
arXiv2010

Cooperation Evolution in Random Multiplicative Environments

Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative noise as opposed to additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. We study the various implications of this observation and its applications in various contexts.

q-fin.GN↗
arXiv2008

The evolution of EU business cycle synchronisation 1981-2007

Most of the analytical techniques used in the business cycle synchronisation literature rely upon the estimation of an empirical correlation matrix of time series data of macroeconomic aggregates, real GDP usually being the key variable. But the small number of available observations and small number of economies mean that the empirical correlation matrix may contain considerable noise. Random matrix theory was developed in physics to overcome this problem. The largest eigenvalue of the correlation matrix informs us directly about the degree to which movements of the economies are genuinely correlated. The evolution of business cycle synchronisation can be analysed with the temporal evolution of the largest eigenvalue over a fixed window of data. I analyse quarterly real GDP data 1981Q1-2008Q1 for the core EU economies - Germany, France, Italy, Spain, Netherlands, Belgium - along with the UK, which is a member of the EU but not the Euro, and the US as a comparator. The core EU economies have shown varying but strong synchronisation over the whole period. In contrast, the UK and the US are much more synchronised with each other than they are with the core EU economies.

q-fin.ST↗
arXiv2008

Market dynamics after large financial crash

The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential $U$ under the influence of the variable noise intensity, depending on the particle position $x$. Based on the empirical data the approximate estimation of the Kramers-Moyal coefficients $D_{1,2}$ allow to predicate quite definitely the behavior of the potential introduced by $D_1 = - \partial U /\partial x$ and the volatility $\sim \sqrt{D_2}$. It has been shown that the presented model describes well enough the best known empirical facts relative to the large financial crash of October 1987. \

q-fin.ST↗
arXiv2008

Is Faith The Enemy Of Science?

In this article, inspired by Lawrence Krauss' plenary talk at the 2007 CAP congress, the relation between faith and science is examined.

physics.pop-ph↗
arXiv2008

The saturation threshold of public opinion: are aggressive media campaigns always effective?

An important aspect that must be considered when studying opinion formation phenomena is the different social attitude of the agents taking part in the process. Different kinds of interconnections and of interacting behaviours should be associated to the agents depending on their opinion: radicals tend to self-segregate but, on the other hand, have a stronger capacity to convince neutral agents. Other important questions arise when the official media strongly promotes one position. The different perception that each agent has of the official information can lead, in case of monopolistic and aggressive media, to a reaction effect in the population that starts to create massive antagonist clusters.

physics.soc-ph↗
arXiv2009

The Ups and Downs of Modeling Financial Time Series with Wiener Process Mixtures

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Lévy distributions; we also show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.

physics.data-an↗
arXiv2008

Taxes in a simple wealth distribution model by inelastically scattering particles

In this work we use an inelastic scattering process of particles to propose a model able to reproduce the salient features of the wealth distribution in an economy by including taxes to each trading process and redistributing that collected among the population according to a given criterion. Additionally, we show that different optimal levels of taxes may exist depending on the redistribution criterion.

q-fin.GN↗
arXiv2009

Scaling properties of complex networks: Toward Wilsonian renormalization for complex networks

Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree distribution of the network changes by two-site scaling. In particular, networks constructed by the BA algorithm behave differently from the networks observed in the nature. In addition, an iterative scaling scheme can define a new renormalizing method. We investigated the possibility of defining the Wilsonian renormalization group method on general complex networks and its application to the analysis of the dynamics of complex networks.

physics.soc-ph↗
arXiv2008

Heterogeneous expectations and long range correlation of the volatility of asset returns

Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection between the distributional properties of the heterogeneity parameters and the auto-covariance/auto-correlation functions of the realized volatility. We report different behaviors, or change of convention, whose observation depends on the market phase under consideration. In particular, we report and justify the fact that the volatility exhibits significantly longer memory during the phases of speculative bubble than during the phase of recovery following the collapse of a speculative bubble.

q-fin.ST↗
arXiv2008

Theory of Zipf's Law and of General Power Law Distributions with Gibrat's law of Proportional Growth

We summarize a book under publication with his title written by the three present authors, on the theory of Zipf's law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request from the authors. For clarity, consistence of language and conciseness, we discuss the origin and conditions of the validity of Zipf's law using the terminology of firms' asset values. We use firms at the entities whose size distributions are to be explained. It should be noted, however, that most of the relations discussed in this book, especially the intimate connection between Zipf's and Gilbrat's laws, underlie Zipf's law in diverse scientific areas. The same models and variations thereof can be straightforwardly applied to any of the other domains of application.

q-fin.GN↗