Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets

Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients, which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are overconfident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.     

Diagnosis and prediction of rebounds in financial markets

We introduce the concept of “negative bubbles” as the mirror (but not necessarily exactly symmetric) image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a hazard rate describing the collective buying pressure of noise traders. The price fall occurring during a transient negative bubble can be interpreted as an effective random down payment that rational agents accept to pay in the hope of profiting from the expected occurrence of a possible rally. We validate the model by showing that it has significant predictive power in identifying the times of major market rebounds. This result is obtained by using a general pattern recognition method that combines the information obtained at multiple times from a dynamical calibration of the JLS model. Error diagrams, Bayesian inference and trading strategies suggest that one can extract genuine information and obtain real skill from the calibration of negative bubbles with the JLS model. We conclude that negative bubbles are in general predictably associated with large rebounds or rallies, which are the mirror images of the crashes terminating standard bubbles.     

Price dynamics from a simple multiplicative random process model

The existence of stylized facts suggests that there might be `universal' mechanism which drives price evolution on financial markets in general. Based on empirical estimates of 10 major indices, we propose a stylized model of endogenous price formation on an aggregate level whose key issue is that price evolution is driven by the `market's' expectations about future growth rates of investment. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics which admits some far reaching formal analysis. Generated return trails exhibit statistical properties such as 'volatility clustering', multi scaling, and a non-Gaussian distribution which is in quantitative in agreement with stylized facts from empirical asset returns. Additionally non-equilibrium entropies are also considered. These results suggests that the structure of the model mimicks a mechanism which is essential in driving price dynamics of financial markets in general.     

Self-organizing Ising model of financial markets

We study a dynamical Ising-like model of agents' opinions (buy or sell) with learning, in which the coupling coefficients are re-assessed continuously in time according to how past external news (time-varying magnetic field) have explained realized market returns. By combining herding, the impact of external news and private information, we find that the stylized facts of financial markets are reproduced only when agents misattribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the Ising critical point.     

Editorial - Constraints: From physical principles to molecular simulations and beyond

The two articles in this issue of the European Physical Journal Special Topics cover topics in Econophysics and GPU computing in the last years. In the first article [1], the formation of market prices for financial assets is described which can be understood as superposition of individual actions of market participants, in which they provide cumulative supply and demand. This concept of macroscopic properties emerging from microscopic interactions among the various subcomponents of the overall system is also well-known in statistical physics. The distribution of price changes in financial markets is clearly non-Gaussian leading to distinct features of the price process, such as scaling behavior, non-trivial correlation functions and clustered volatility. This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.     

Contagion effects in a chartist-fundamentalist model with time delays

In this paper two models of speculative markets are developed to study the effects of feedback mechanisms in financial markets. In the first model, a crash market model couples a linear chartist-fundamentalist model with time delays with a log-periodic market index I(t) through direct coupling. Numerical solutions to the model show that asset prices exhibit significant persistence as a result of the coupling to the log-periodic market index. An extension to include endogenous wealth dynamics shows that the chartists benefit from the persistent dynamics induced by the coupling. The second model is a two-asset model represented by a 2-dimensional delay-differential equation. Asset one price exhibits limit cycle dynamics while in the second market asset prices follow stable damped oscillations. The markets are coupled through a diffusive coupling term. Solutions to the coupled model show that the dynamics of asset two changes fundamentally with the price now exhibiting a limit cycle. The stable converging dynamics is replaced with limit cycle oscillations around the fundamental.     

The Stock Market Model with Delayed Information Impact from a Socioeconomic View

Finding the critical factor and possible “Newton’s laws” in financial markets has been an important issue. However, with the development of information and communication technologies, financial models are becoming more realistic but complex, contradicting the objective law “Greatest truths are the simplest.” Therefore, this paper presents an evolutionary model independent of micro features and attempts to discover the most critical factor. In the model, information is the only critical factor, and stock price is the emergence of collective behavior. The statistical properties of the model are significantly similar to the real market. It also explains the correlations of stocks within an industry, which provides a new idea for studying critical factors and core structures in the financial markets.     

GPU-computing in econophysics and statistical physics

This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.     

Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis

In order to study the universality of the interactions among different markets, we analyze the cross-correlation matrix of the price of the Chinese and American bank stocks. We then find that the stock prices of the emerging market are more correlated than that of the developed market. Considering that the values of the components for the eigenvector may be positive or negative, we analyze the differences between two markets in combination with the endogenous and exogenous events which influence the financial markets. We find that the sparse pattern of components of eigenvectors out of the threshold value has no change in American bank stocks before and after the subprime crisis. However, it changes from sparse to dense for Chinese bank stocks. By using the threshold value to exclude the external factors, we simulate the interactions in financial markets.     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.     

Twitter Sentiment Analysis and Influence on Stock Performance Using Transfer Entropy and EGARCH Methods

Financial economic research has extensively documented the fact that the impact of the arrival of negative news on stock prices is more intense than that of the arrival of positive news. The authors of the present study followed an innovative approach based on the utilization of two artificial intelligence algorithms to test that asymmetric response effect. Methods: The first algorithm was used to web-scrape the social network Twitter to download the top tweets of the 24 largest market-capitalized publicly traded companies in the world during the last decade. A second algorithm was then used to analyze the contents of the tweets, converting that information into social sentiment indexes and building a time series for each considered company. After comparing the social sentiment indexes’ movements with the daily closing stock price of individual companies using transfer entropy, our estimations confirmed that the intensity of the impact of negative and positive news on the daily stock prices is statistically different, as well as that the intensity with which negative news affects stock prices is greater than that of positive news. The results support the idea of the asymmetric effect that negative sentiment has a greater effect than positive sentiment, and these results were confirmed with the EGARCH model.     

Multifractal detrended fluctuation analysis of derivative and spot markets

We investigate the multifractal properties of price increments in the cases of derivative and spot markets. Through the multifractal detrended fluctuation analysis, we estimate the generalized Hurst and the Renyi exponents for price fluctuations. By deriving the singularity spectrum from the above exponents, we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets. The different behavior of each agent-group in transactions is also discussed. In order to identify the nature of the underlying multifractality, we apply the method of surrogate data to both sets of financial data. It is shown that multifractality due to a fat-tailed distribution is significant.     

Majority orienting model for the oscillation of market price

The present paper introduces a majority orienting model in which the dealers behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the van der Pol equation which is a deterministic approximation of our model.Received: 29 October 2003, Published online: 15 March 2004PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 05.45.Tp Time series analysis - 02.50.Ey Stochastic processesY. Itoh: Also at The Graduate University for Advanced Studies     

Coupled effects of market impact and asymmetric sensitivity in financial markets

By incorporating market impact and asymmetric sensitivity into the evolutionary minority game, we study the coevolutionary dynamics of stock prices and investment strategies in financial markets. Both the stock price movement and the investors’ global behavior are found to be closely related to the phase region they fall into. Within the region where the market impact is small, investors’ asymmetric response to gains and losses leads to the occurrence of herd behavior, when all the investors are prone to behave similarly in an extreme way and large price fluctuations occur. A linear relation between the standard deviation of stock price changes and the mean value of strategies is found. With full market impact, the investors tend to self-segregate into opposing groups and the introduction of asymmetric sensitivity leads to the disappearance of dominant strategies. Compared with the situations in the stock market with little market impact, the stock price fluctuations are suppressed and an efficient market occurs. Theoretical analyses indicate that the mechanism of phase transition from clustering to self-segregation in the present model is similar to that in the majority–minority game and the occurrence and disappearance of efficient markets are related to the competition between the trend-following and the trend-aversion forces. The clustering of the strategies in the present model results from the majority-wins effect and the wealth-driven mechanism makes the market become predictable.     

The subtle nature of financial random walks

We first review the most important "stylized facts" of financial time series, that turn out to be, to a large extent, universal. We then recall how the multifractal random walk of Bacry, Muzy, and Delour generalizes the standard model of financial price changes and accounts in an elegant way for many of their empirical properties. In a second part, we provide empirical evidence for a very subtle compensation mechanism that underlies the random nature of price changes. This compensation drives the market close to a critical point, that may explain the sensitivity of financial markets to small perturbations, and their propensity to enter bubbles and crashes. We argue that the resulting unpredictability of price changes is very far from the neoclassical view that markets are informationally efficient.     

Minimal agent based model for financial markets I

We introduce a minimal agent based model for financial markets to understand the nature and self-organization of the stylized facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the most important deviations of price time series from a random walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The stylized facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effects which, however, can occur at different time scales. We propose a new mechanism for the self-organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represents a crucial element for this state of self-organized intermittency. The model can be easily generalized to consider more realistic variants.     

Dynamical mechanism of two-phase phenomena in financial markets

Two-phase behavior of the Korean treasury bond (KTB) futures in the Korean exchange market is investigated in this study. To show that the two-phase phenomena are due to heavy-tailed behavior of distribution of price returns, actual data from the KTB futures market with shuffled data and a generated time series are examined according to the Brownian process. In addition, we study the correlation inherent in the KTB futures and its Brownian walk, describing the extent to which the volatility clustering plays a crucial role in equilibrium and nonequilibrium states of financial markets. It is shown that the two-phase behavior essentially results from heavy-tailed behavior of the distribution of price returns. This two-phase behavior does not appear to be relevant to volatility clustering.     

The Linear Relationship Model with LASSO for Studying Stock Networks

The correlation-based network is a powerful tool to reveal the influential mechanisms and relations in stock markets. However, current methods for developing network models are dominantly based on the pairwise relationship of positive correlations. This work proposes a new approach for developing stock relationship networks by using the linear relationship model with LASSO to explore negative correlations under a systemic framework. The developed model not only preserves positive links with statistical significance but also includes link directions and negative correlations. We also introduce blends cliques with the balance theory to investigate the consistency properties of the developed networks. The ASX 200 stock data with 194 stocks are applied to evaluate the effectiveness of our proposed method. Results suggest that the developed networks not only are highly consistent with the correlation coefficient in terms of positive or negative correlations but also provide influence directions in stock markets.     

Statistical properties of agent-based models in markets with continuous double auction mechanism

Real world markets display power-law features in variables such as price fluctuations in stocks. To further understand market behavior, we have conducted a series of market experiments on our web-based prediction market platform which allows us to reconstruct transaction networks among traders. From these networks, we are able to record the degree of a trader, the size of a community of traders, the transaction time interval among traders and other variables that are of interest. The distributions of all these variables show power-law behavior. On the other hand, agent-based models have been proposed to study the properties of real financial markets. We here study the statistical properties of these agent-based models and compare them with the results from our web-based market experiments. In this work, three agent-based models are studied, namely, zero-intelligence (ZI), zero-intelligence-plus (ZIP) and Gjerstad-Dickhaut (GD). Computer simulations of variables based on these three agent-based models were carried out. We found that although being the most naive agent-based model, ZI indeed best describes the properties observed in real markets. Our study suggests that the basic ingredient to produce the observed properties from real world markets could in fact be the result of a continuously evolving dynamical system with basic features similar to the ZI model.