Quantifying Stock Return Distributions in Financial Markets

Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.     

Statistical Properties and Pre-Hit Dynamics of Price Limit Hits in the Chinese Stock Markets

Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders’ short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of price limit hits are not well studied partially due to the fact that main stock markets such as the US markets and most European markets do not set price limits. Here, we perform detailed analyses of the high-frequency data of all A-share common stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange from 2000 to 2011 to investigate the statistical properties of price limit hits and the dynamical evolution of several important financial variables before stock price hits its limits. We compare the properties of up-limit hits and down-limit hits. We also divide the whole period into three bullish periods and three bearish periods to unveil possible differences during bullish and bearish market states. To uncover the impacts of stock capitalization on price limit hits, we partition all stocks into six portfolios according to their capitalizations on different trading days. We find that the price limit trading rule has a cooling-off effect (object to the magnet effect), indicating that the rule takes effect in the Chinese stock markets. We find that price continuation is much more likely to occur than price reversal on the next trading day after a limit-hitting day, especially for down-limit hits, which has potential practical values for market practitioners.     

A Financial Market Model Incorporating Herd Behaviour

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents’ accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents’ accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.     

Confidence and the Stock Market: An Agent-Based Approach

Using a behavioral finance approach we study the impact of behavioral bias. We construct an artificial market consisting of fundamentalists and chartists to model the decision-making process of various agents. The agents differ in their strategies for evaluating stock prices, and exhibit differing memory lengths and confidence levels. When we increase the heterogeneity of the strategies used by the agents, in particular the memory lengths, we observe excess volatility and kurtosis, in agreement with real market fluctuations—indicating that agents in real-world financial markets exhibit widely differing memory lengths. We incorporate the behavioral traits of adaptive confidence and observe a positive correlation between average confidence and return rate, indicating that market sentiment is an important driver in price fluctuations. The introduction of market confidence increases price volatility, reflecting the negative effect of irrationality in market behavior.     

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.     

Being on the Field When the Game Is Still Under Way. The Financial Press and Stock Markets in Times of Crisis

This paper looks at the relationship between negative news and stock markets in times of global crisis, such as the 2008/2009 period. We analysed one year of front page banner headlines of three financial newspapers, the Wall Street Journal, Financial Times, and Il Sole24ore to examine the influence of bad news both on stock market volatility and dynamic correlation. Our results show that the press and markets influenced each other in generating market volatility and in particular, that the Wall Street Journal had a crucial effect both on the volatility and correlation between the US and foreign markets. We also found significant differences between newspapers in their interpretation of the crisis, with the Financial Times being significantly pessimistic even in phases of low market volatility. Our results confirm the reflexive nature of stock markets. When the situation is uncertain and unpredictable, market behaviour may even reflect qualitative, big picture, and subjective information such as streamers in a newspaper, whose economic and informative value is questionable.     

How Volatilities Nonlocal in Time Affect the Price Dynamics in Complex Financial Systems

What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made, it remains challenging. Physicists usually apply the concepts and methods in statistical physics, such as temporal correlation functions, to study financial dynamics. However, the usual volatility-return correlation function, which is local in time, typically fluctuates around zero. Here we construct dynamic observables nonlocal in time to explore the volatility-return correlation, based on the empirical data of hundreds of individual stocks and 25 stock market indices in different countries. Strikingly, the correlation is discovered to be non-zero, with an amplitude of a few percent and a duration of over two weeks. This result provides compelling evidence that past volatilities nonlocal in time affect future returns. Further, we introduce an agent-based model with a novel mechanism, that is, the asymmetric trading preference in volatile and stable markets, to understand the microscopic origin of the volatility-return correlation nonlocal in time.     

Degree-Strength Correlation Reveals Anomalous Trading Behavior

Manipulation is an important issue for both developed and emerging stock markets. Many efforts have been made to detect manipulation in stock markets. However, it is still an open problem to identify the fraudulent traders, especially when they collude with each other. In this paper, we focus on the problem of identifying the anomalous traders using the transaction data of eight manipulated stocks and forty-four non-manipulated stocks during a one-year period. By analyzing the trading networks of stocks, we find that the trading networks of manipulated stocks exhibit significantly higher degree-strength correlation than the trading networks of non-manipulated stocks and the randomized trading networks. We further propose a method to detect anomalous traders of manipulated stocks based on statistical significance analysis of degree-strength correlation. Experimental results demonstrate that our method is effective at distinguishing the manipulated stocks from non-manipulated ones. Our method outperforms the traditional weight-threshold method at identifying the anomalous traders in manipulated stocks. More importantly, our method is difficult to be fooled by colluded traders.     

Dynamic Evolution of Cross-Correlations in the Chinese Stock Market

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.     

Does corn market uncertainty impact the US ethanol prices?

The growing interest in biofuel as a green energy source has intensified the linkages between corn and ethanol markets, especially in the United States that represents the largest producing and exporting country for ethanol in the world. In this study, we examine the effect of corn market uncertainty on the price changes of US ethanol applying a set of GARCH‐jump models. We find that the US ethanol price changes react positively to the corn market volatility shocks after controlling for the effect of oil price uncertainty. In addition, we document that the impact of corn price volatility on the US ethanol prices appears to be asymmetric. Specifically, only the positive corn market volatility shocks are found to influence the ethanol market returns. Our findings also suggest that time‐varying jumps do exist in the ethanol market.     

Exploring Market State and Stock Interactions on the Minute Timescale

A stock market is a non-stationary complex system. The stock interactions are important for understanding the state of the market. However, our knowledge on the stock interactions on the minute timescale is limited. Here we apply the random matrix theory and methods in complex networks to study the stock interactions and sector interactions. Further, we construct a new kind of cross-correlation matrix to investigate the correlation between the stock interactions at different minutes within one trading day. Based on 50 million minute-to-minute price data in the Shanghai stock market, we discover that the market states in the morning and afternoon are significantly different. The differences mainly exist in three aspects, i.e. the co-movement of stock prices, interactions of sectors and correlation between the stock interactions at different minutes. In the afternoon, the component stocks of sectors are more robust and the structure of sectors is firmer. Therefore, the market state in the afternoon is more stable. Furthermore, we reveal that the information of the sector interactions can indicate the financial crisis in the market, and the indicator based on the empirical data in the afternoon is more effective.     

High Quality Topic Extraction from Business News Explains Abnormal Financial Market Volatility

Understanding the mutual relationships between information flows and social activity in society today is one of the cornerstones of the social sciences. In financial economics, the key issue in this regard is understanding and quantifying how news of all possible types (geopolitical, environmental, social, financial, economic, etc.) affects trading and the pricing of firms in organized stock markets. In this article, we seek to address this issue by performing an analysis of more than 24 million news records provided by Thompson Reuters and of their relationship with trading activity for 206 major stocks in the S&P US stock index. We show that the whole landscape of news that affects stock price movements can be automatically summarized via simple regularized regressions between trading activity and news information pieces decomposed, with the help of simple topic modeling techniques, into their “thematic” features. Using these methods, we are able to estimate and quantify the impacts of news on trading. We introduce network-based visualization techniques to represent the whole landscape of news information associated with a basket of stocks. The examination of the words that are representative of the topic distributions confirms that our method is able to extract the significant pieces of information influencing the stock market. Our results show that one of the most puzzling stylized facts in financial economies, namely that at certain times trading volumes appear to be “abnormally large,” can be partially explained by the flow of news. In this sense, our results prove that there is no “excess trading,” when restricting to times when news is genuinely novel and provides relevant financial information.     

Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth

Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator.     

Analyzing the Long Term Cohesive Effect of Sector Specific Driving Forces

Financial markets are partially composed of sectors dominated by external driving forces, such as commodity prices, infrastructure and other indices. We characterize the statistical properties of such sectors and present a novel model for the coupling of the stock prices and their dominating driving forces, inspired by mean reverting stochastic processes. Using the model we were able to explain the market sectors’ long term behavior and estimate the coupling strength between stocks in financial markets and the sector specific driving forces. Notably, the analysis was successfully applied to the shipping market, in which the Baltic dry index (BDI), an assessment of the price of transporting the major raw materials by sea, influences the shipping financial market. We also present the analysis of other sectors—the gold mining market and the food production market, for which the model was also successfully applied. The model can serve as a general tool for characterizing the coupling between external forces and affected financial variables and therefore for estimating the risk in sectors and their vulnerability to external stress.     

Unraveling Hidden Order in the Dynamics of Developed and Emerging Markets

The characterization of asset price returns is an important subject in modern finance. Traditionally, the dynamics of stock returns are assumed to lack any temporal order. Here we present an analysis of the autocovariance of stock market indices and unravel temporal order in several major stock markets. We also demonstrate a fundamental difference between developed and emerging markets in the past decade - emerging markets are marked by positive order in contrast to developed markets whose dynamics are marked by weakly negative order. In addition, the reaction to financial crises was found to be reversed among developed and emerging markets, presenting large positive/negative autocovariance spikes following the onset of these crises. Notably, the Chinese market shows neutral or no order while being regarded as an emerging market. These findings show that despite the coupling between international markets and global trading, major differences exist between different markets, and demonstrate that the autocovariance of markets is correlated with their stability, as well as with their state of development.     

Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market

What are the dominant stocks which drive the correlations present among stocks traded in a stock market? Can a correlation analysis provide an answer to this question? In the past, correlation based networks have been proposed as a tool to uncover the underlying backbone of the market. Correlation based networks represent the stocks and their relationships, which are then investigated using different network theory methodologies. Here we introduce a new concept to tackle the above question—the partial correlation network. Partial correlation is a measure of how the correlation between two variables, e.g., stock returns, is affected by a third variable. By using it we define a proxy of stock influence, which is then used to construct partial correlation networks. The empirical part of this study is performed on a specific financial system, namely the set of 300 highly capitalized stocks traded at the New York Stock Exchange, in the time period 2001–2003. By constructing the partial correlation network, unlike the case of standard correlation based networks, we find that stocks belonging to the financial sector and, in particular, to the investment services sub-sector, are the most influential stocks affecting the correlation profile of the system. Using a moving window analysis, we find that the strong influence of the financial stocks is conserved across time for the investigated trading period. Our findings shed a new light on the underlying mechanisms and driving forces controlling the correlation profile observed in a financial market.     

Cross-Correlation Asymmetries and Causal Relationships between Stock and Market Risk

We study historical correlations and lead-lag relationships between individual stock risk (volatility of daily stock returns) and market risk (volatility of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over all stocks, using 71 stock prices from the Standard & Poor''s 500 index for 1994–2013. We focus on the behavior of the cross-correlations at the times of financial crises with significant jumps of market volatility. The observed historical dynamics showed that the dependence between the risks was almost linear during the US stock market downturn of 2002 and after the US housing bubble in 2007, remaining at that level until 2013. Moreover, the averaged cross-correlation function often had an asymmetric shape with respect to zero lag in the periods of high correlation. We develop the analysis by the application of the linear response formalism to study underlying causal relations. The calculated response functions suggest the presence of characteristic regimes near financial crashes, when the volatility of an individual stock follows the market volatility and vice versa.     

Association between Stock Market Gains and Losses and Google Searches

Experimental studies in the area of Psychology and Behavioral Economics have suggested that people change their search pattern in response to positive and negative events. Using Internet search data provided by Google, we investigated the relationship between stock-specific events and related Google searches. We studied daily data from 13 stocks from the Dow-Jones and NASDAQ100 indices, over a period of 4 trading years. Focusing on periods in which stocks were extensively searched (Intensive Search Periods), we found a correlation between the magnitude of stock returns at the beginning of the period and the volume, peak, and duration of search generated during the period. This relation between magnitudes of stock returns and subsequent searches was considerably magnified in periods following negative stock returns. Yet, we did not find that intensive search periods following losses were associated with more Google searches than periods following gains. Thus, rather than increasing search, losses improved the fit between people’s search behavior and the extent of real-world events triggering the search. The findings demonstrate the robustness of the attentional effect of losses.     

Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery

We present a dynamical model of a spatial fishery describing the time evolution of the fish stock, the fishing effort and the market price of the resource. The market price is fixed by the gap between the supply and the demand. Assuming two time scales, we use “aggregation of variables methods” in order to derive a reduced model governing fish density and fishing effort at a slow time scale. The bifurcation analysis of the reduced model is performed. According to parameters values, three main cases can occur: (i) a stable fishery free equilibrium, (ii) a stable persistent fishery equilibrium and (iii) coexistence of three strictly positive equilibria, two of them being stable separated by a saddle. In this last case, a stable equilibrium corresponds to a traditional fishery with large fish stock, small fishing effort and small market price. The second stable one corresponds to over-exploitation of the resource with small fish stock, large fishing effort and large market price.     

Web search queries can predict stock market volumes

We live in a computerized and networked society where many of our actions leave a digital trace and affect other people's actions. This has lead to the emergence of a new data-driven research field: mathematical methods of computer science, statistical physics and sociometry provide insights on a wide range of disciplines ranging from social science to human mobility. A recent important discovery is that search engine traffic (i.e., the number of requests submitted by users to search engines on the www) can be used to track and, in some cases, to anticipate the dynamics of social phenomena. Successful examples include unemployment levels, car and home sales, and epidemics spreading. Few recent works applied this approach to stock prices and market sentiment. However, it remains unclear if trends in financial markets can be anticipated by the collective wisdom of on-line users on the web. Here we show that daily trading volumes of stocks traded in NASDAQ-100 are correlated with daily volumes of queries related to the same stocks. In particular, query volumes anticipate in many cases peaks of trading by one day or more. Our analysis is carried out on a unique dataset of queries, submitted to an important web search engine, which enable us to investigate also the user behavior. We show that the query volume dynamics emerges from the collective but seemingly uncoordinated activity of many users. These findings contribute to the debate on the identification of early warnings of financial systemic risk, based on the activity of users of the www.