Tribes under Threat – The Collective Behavior of Firms During the Stock Market Crisis

Due to their unpredictable behavior, stock markets are examples of complex systems. Yet, the dominant analysis of these markets as- sumes simple stochastic variations, eventually tainted by short-lived memory. This paper proposes an alternative strategy, based on a stochastic geometry de¯ning a robust index of the structural dynamics of the markets and based on notions of topology de¯ning a new coef- ficient that identifies the structural changes occurring on the S&P500 set of stocks. The results demonstrate the consistency of the random hypothesis as applied to normal periods but they also show its in- adequacy as to the analysis of periods of turbulence, for which the emergence of collective behavior of sectoral clusters of firms is mea- sured. This behavior is identified as a meta-routine.

Bargaining clouds, or mathematics as a metaphoric exploration of the unexpected

In the very first page of his highly regarded novel, One Hundred Years of Solitude, Gabriel Garcia Marquez writes that, when arriving at Macondo and discovering so many unknown objects, Aurelio Buendia had to point out these things because no words were defined for them. This metaphor of the process of metaphorisation is an apt description of the scientific process itself, as science points out to what it ignores: denotation generates connotation. Even when science is defined as a self-contained logic, as mathematics once presumed to be, it dares into the territories of the unknown and of the unexpected; the more rigorous, the more daring it ought to be. In this paper, we argue that this metaphor is powerful enough to suggest new methods to interpret the emergence of new patterns. In the current example, a stochastic geometry and topological technique are used to describe the structural change in the stock market for the last years. This new method suggests evidence for a transition of regimes in these markets, measures its dynamics and metaphorically provides a graphic description of the ongoing process

Tribes under threat : the collective behavior of firms during the stock market crisis

Due to their unpredictable behavior, stock markets are examples of complex systems. Yet, the dominant analysis of these markets as- sumes simple stochastic variations, eventually tainted by short-lived memory. This paper proposes an alternative strategy, based on a stochastic geometry defining a robust index of the structural dynamics of the markets and based on notions of topology defining a new coef- ficient that identifies the structural changes occurring on the S&P500 set of stocks. The results demonstrate the consistency of the random hypothesis as applied to normal periods but they also show its in- adequacy as to the analysis of periods of turbulence, for which the emergence of collective behavior of sectoral clusters of firms is mea- sured. This behavior is identified as a meta-routine

Complex behavior of stock markets : processes of synchronization and desynchronization during crises

This paper investigates the dynamics of in the S&P500 index from daily returns for the last 30 years. Using a stochastic geometry technique, each S&P500 yearly batch of data is embedded in a subspace that can be accurately described by a reduced number of dimensions. Such feature is understood as empirical evidence for the presence of a certain amount of structure in the market. As part of the inquiry into the structure of the market we investigate changes in its volume and shape, and we define new measures for that purpose. Having these measures defined in the space of stocks we analyze the effects of some extreme phenomena on the geometry of the market. We discuss the hypothesis that collective behavior in period of crises reinforces the structure of correlations between stocks, but that it also may have an opposite effect on clustering by similar economic sectors. Comparing the crises of 1987 and 2001, we discuss why the expansion of the ellipsoid describing the geometry of the distances in the market, which occurs in the latter period, is not homogeneous through sectors. The conclusions from this research identify some of the changes in the structure of the market over the last 30 yearsinfo:eu-repo/semantics/publishedVersio

The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises

This paper investigates the dynamics of stocks in the S&P500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose, which is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of the crises. With this measure, we analyze the effects of some extreme phenomena on the geometry of the market. Nine crashes between 1987 and 2001 are compared by looking at the way they modify the shape of the manifold that describes the S&P500 market space. These crises are identified as (a) structural, (b) general and (c) local

The geometry of crashes : A measure of the dynamics of stock market crises

Lodres : Taylor & Francis Group, 2007 ResumoThis paper investigates the dynamics of stocks in the S&P 500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose that is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of crises. With this measure, we analyse the effects of extreme phenomena on the geometry of the market. Nine crashes between 1987 and 2001 are compared by looking at the way they modify the shape of the manifold that describes the S&P 500 market space..info:eu-repo/semantics/publishedVersio

The Seismography of Crashes in Financial Markets

This paper investigates the dynamics of stocks in the S&P500 for the last 33 years, considering the population of all companies present in the index for the whole period. Using a stochastic geometry tech¬nique and defining a robust index of the dynamics of the market struc¬ture, which is able to provide information about the intensity of the crises, the paper proposes a seismographic classification of the crashes that occurred during the period. The index is used in order to inves¬tigate and to classify the impact of the twelve crashes between July 1973 and March 2006 and to discuss the available evidence of change of structure after the fin de sicle