Universal Behavior of Extreme Price Movements in Stock Markets

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.Comment: 4 pages, 3 figure

Noise-induced phase transitions: Effects of the noises' statistics and spectrum

The local, uncorrelated multiplicative noises driving a second-order, purely noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The potential scientific and technological interest of this phenomenon calls for a study of the effects of the noises' statistics and spectrum. This task is facilitated if these noises are dynamically generated by means of stochastic differential equations (SDE) driven by white noises. One such case is that of Ornstein--Uhlenbeck noises which are stationary, with Gaussian pdf and a variance reduced by the self-correlation time (\tau), and whose effect on the NIPT phase diagram has been studied some time ago. Another such case is when the stationary pdf is a (colored) Tsallis' (q)--\emph{Gaussian} which, being a \emph{fat-tail} distribution for (q>1) and a \emph{compact-support} one for (q<1), allows for a controlled exploration of the effects of the departure from Gaussian statistics. As done before with stochastic resonance and other phenomena, we now exploit this tool to study--within a simple mean-field approximation and with an emphasis on the \emph{order parameter} and the ``\emph{susceptibility}''--the combined effect on NIPT of the noises' statistics and spectrum. Even for relatively small (\tau), it is shown that whereas fat-tail noise distributions ((q>1)) counteract the effect of self-correlation, compact-support ones ((q<1)) enhance it. Also, an interesting effect on the susceptibility is seen in the last case.Comment: 6 pages, 10 figures, uses aipproc.cls, aip-8s.clo and aipxfm.sty. To appear in AIP Conference Proceedings. Invited talk at MEDYFINOL'06 (XV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics

Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points

We determine the limit distributions of sums of deterministic chaotic variables in unimodal maps assisted by a novel renormalization group (RG) framework associated to the operation of increment of summands and rescaling. In this framework the difference in control parameter from its value at the transition to chaos is the only relevant variable, the trivial fixed point is the Gaussian distribution and a nontrivial fixed point is a multifractal distribution with features similar to those of the Feigenbaum attractor. The crossover between the two fixed points is discussed and the flow toward the trivial fixed point is seen to consist of a sequence of chaotic band mergers.Comment: 7 pages, 2 figures, to appear in Journal of Physics: Conf.Series (IOP, 2010

Living in an Irrational Society: Wealth Distribution with Correlations between Risk and Expected Profits

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an ``irrational'' behavior risking more than reasonable.Comment: 7 pages, 8 figure

Modeling bone healing by boundary element method

El proceso de curación de fracturas es iniciado y regulado principalmente por los factores de crecimiento y por el entorno mecánico en el callo. Este fenómeno ha sido analizado desde un punto de vista biomecánico. La mayoría de los modelos computacionales están basados en el método de los elementos finitos y muchos de ellos estudian los niveles de tensiones y deformaciones producidos en los diferentes tejidos como el principal estímulo mecánico que afecta la diferenciación celular y el patrón de osificación ósea. En este trabajo se incorporó esa hipótesis en un entorno basado en el método de los elementos de contorno (BEM) para problemas axialmente simétricos. La idea principal es proponer el método de elementos de contorno como una alternativa atractiva a los métodos de dominio comúnmente utilizados en esta clase de problemas: diferencias finitas y elementos finitos. Los resultados obtenidos fueron cotejados con los reportados por la literatura comprobando la versatilidad y efectividad del método numérico propuesto. Como una primera aproximación, se realizó un análisis elástico-lineal para modelar los efectos de estimulación e inhibición que ejerce el estado de deformación sobre el proceso de diferenciación tisular, siguiendo la metodología propuesta por Claes and Heigele. Luego, en un modelo bifásico poroelástico en régimen estacionario, se incorpora la presión de poro como variable adicional dentro de la hipótesis, lo que permitió complementar las conclusiones hechas por Claes and Heigele. De esta manera, existe una nueva correlación de valores que permitirán a los modelos actuales comparar la evolución de propiedades tales como el modulo de elasticidad (E) y relación de Poisson (À), en base al estado de deformación presente en el modelo en análisis poroelásticos.Peer Reviewe

Nonequilibrium evolution of volatility in origination and extinction explains fat-tailed fluctuations in Phanerozoic biodiversity

Fluctuations in biodiversity, large and small, pervade the fossil record, yet we do not understand the processes generating them. Here, we extend theory from nonequilibrium statistical physics to describe the fat-tailed form of fluctuations in Phanerozoic marine invertebrate richness. Using this theory, known as superstatistics, we show that heterogeneous rates of origination and extinction between clades and conserved rates within clades account for this fat-tailed form. We identify orders and families as the taxonomic levels at which clades experience interclade heterogeneity and within-clade homogeneity of rates, indicating that families are subsystems in local statistical equilibrium, while the entire system is not. The separation of timescales between within-clade background rates and the origin of major innovations producing new orders and families allows within-clade dynamics to reach equilibrium, while between-clade dynamics do not. The distribution of different dynamics across clades is consistent with niche conservatism and pulsed exploration of adaptive landscapes.Fil: Rominger, Andrew J.. No especifíca;Fil: Fuentes, Miguel Angel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; Argentina. Universidad San Sebastián; ChileFil: Marquet, Pablo A.. Pontificia Universidad Católica de Chile; Chile. Instituto de Ecología y Biodiversidad; Chile. Universidad Nacional Autónoma de México; Méxic

Abecedario esencial. Anne Berning: Encyclopaedic Incompleteness

Gran parte del legado cultural que nos precede y al tiempo nos ilumina está presente en los libros; entendamos estos como enormes contenedores de sabiduría en los que se hace necesario volver con insistencia para encontrar respuestas, dando rienda suelta a los anhelos de una incipiente curiosidad

Geografías del agua: Del inconsciente estático a la mirada líquida

Es posible que la delicada orografía sobre la que se alza gran parte de la producción contemporánea sea tan sólo un pequeño rescoldo de otras presencias, acaso estancias por las que transita el artista mientras la realidad se nutre de su imaginación allá en el exterior, allá en las proximidades de la creación misma