The minute fluctuations of of S&P 500 and NASDAQ 100 indices display Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a {\em market temperature} for either sign. With increasing time the sharp Boltzmann peak broadens into a Gaussian whose volatility $ σ$ measured in $1/ \sqrt{\rm min}$ is related to the temperature $T$ by $T= σ/ \sqrt{2}$. Plots over the years 1990--2006 show that the arrival of the 2000 crash was preceded by an increase in market temperature, suggesting that this increase can be used as a warning signal for crashes. A plot of the Dow Jones temperature over 78 years reveals a remarkable stability through many historical turmoils, interrupted only by short heat bursts near the crashes.
We study the temporal evolution of the market efficiency in the stock markets using the complexity, entropy density, standard deviation, autocorrelation function, and probability distribution of the log return for Standard and Poor's 500 (S&P 500), Nikkei stock average index, and Korean composition stock price index (KOSPI). Based on the microscopic spin model, we also find that these statistical quantities in stock markets depend on the market efficiency.
Geography effect is investigated for the Chinese stock market including the Shanghai and Shenzhen stock markets, based on the daily data of individual stocks. The Shanghai city and the Guangdong province can be identified in the stock geographical sector. By investigating a geographical correlation on a geographical parameter, the stock location is found to have an impact on the financial dynamics, except for the financial crisis time of the Shenzhen market. Stock distance effect is further studied, with a crossover behavior observed for the stock distance distribution. The probability of the …
The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this, we introduce a market model consisting of randomly fluctuating stocks that occasionally synchronize their short term draw-downs. These synchronous events are parameterized by a ``fear factor'', that reflects the occurrence of dramatic external events which affect the financial market.
Summarized by the efficient market hypothesis, the idea that stock prices fully reflect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efficiency of stock markets, most studies assume this efficiency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we define the time-varying efficiency of stock markets by calculating the permutation entropy within sliding time-windows of log-returns of stock market indices. We show that major world stock …
We investigate the strength and the direction of information transfer in the U.S. stock market between the composite stock price index of stock market and prices of individual stocks using the transfer entropy. Through the directionality of the information transfer, we find that individual stocks are influenced by the index of the market.
In the age of globalization, it is natural that the stock market of each country is not independent form the other markets. In this case, collective behavior could be emerged form their dependency together. This article studies the collective behavior of a set of forty influential markets in the world economy with the aim of exploring a global financial structure that could be called world-stock-market network. Towards this end, we analyze the cross-correlation matrix of the indices of these forty markets using Random Matrix Theory (RMT). We find the degree of collective behavior among the mar…
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TA…
Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry generating component of the conditional probability distribution result in the "elementary" market mill pattern. This asymmetry generating component matches the empirical distribution obtained from the market data. We d…
We investigated the temporally evolving network structures of the Japanese and Korean stock markets through the minimum spanning trees composed of listed stocks. We tested the validity of conventional grouping by industrial categories, and found a common trend of decrease for Japan and Korea. This phenomenon supports the increasing external effects on the markets due to the globalization of both countries. At last the Korean market are grouped with the MSCI Korea Index, a good reference for foreigners' trading, in the early 2000s \cite{Jung2006}. In the Japanese market, this tendency is streng…
Although the threshold network is one of the most used tools to characterize the underlying structure of a stock market, the identification of the optimal threshold to construct a reliable stock network remains challenging. In this paper, the concept of dynamic consistence between the threshold network and the stock market is proposed. The optimal threshold is estimated by maximizing the consistence function. The application of this procedure to stocks belonging to Standard \& Pool's 500 Index from January 2006 to December 2011 yields the threshold value 0.28. In analyzing topological characte…
The daily volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well long-term trends. We also model the transition to a Gaussian distribution for longer time intervals, like months instead of days.
Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and averaged over stock-pairs and time. The results indicate a general trend: whenever the stock index is falling the stock prices are changing in a more correlated manner than in case the stock index is ascending. A thorough statistical analysis of the data shows that the observed differ…
In this study, we establish a network structure of the Korean stock market, one of the emerging markets, with its minimum spanning tree through the correlation matrix. Base on this analysis, it is found that the Korean stock market doesn't form the clusters of the business sectors or of the industry categories. When the MSCI (Morgan Stanley Capital International Inc.) index is exploited, we found that the clusters of the Korean stock market is formed. This finding implicates that the Korean market, in this context, is characteristically different form the mature markets.
We propose improved methods to identify stock groups using the correlation matrix of stock price changes. By filtering out the marketwide effect and the random noise, we construct the correlation matrix of stock groups in which nontrivial high correlations between stocks are found. Using the filtered correlation matrix, we successfully identify the multiple stock groups without any extra knowledge of the stocks by the optimization of the matrix representation and the percolation approach to the correlation-based network of stocks. These methods drastically reduce the ambiguities while finding …
In terms of transfer entropy, we investigated the strength and the direction of information transfer in the US stock market. Through the directionality of the information transfer, the more influential company between the correlated ones can be found and also the market leading companies are selected. Our entropy analysis shows that the companies related with energy industries such as oil, gas, and electricity influence the whole market.
The crowd panic and its contagion play non-negligible roles at the time of the stock crash, especially for China where inexperienced investors dominate the market. However, existing models rarely consider investors in networking stocks and accordingly miss the exact knowledge of how panic contagion leads to abrupt crash. In this paper, by networking stocks of sharing common mutual funds, a new methodology of investigating the market crash is presented. It is surprisingly revealed that the herding, which origins in the mimic of seeking for high diversity across investment strategies to lower in…
In a stock market, the price fluctuations are interactive, that is, one listed company can influence others. In this paper, we seek to study the influence relationships among listed companies by constructing a directed network on the basis of Chinese stock market. This influence network shows distinct topological properties, particularly, a few large companies that can lead the tendency of stock market are recognized. Furthermore, by analyzing the subnetworks of listed companies distributed in several significant economic sectors, it is found that the influence relationships are totally differ…
We study the inter-stock correlations for the largest companies listed on Warsaw Stock Exchange and included in the WIG20 index. Our results from the correlation matrix analysis indicate that the Polish stock market can be well described by a one factor model. We also show that the stock-stock correlations tend to increase with the time scale of returns and they approach a saturation level for the time scales of at least 200 min, i.e. an order of magnitude longer than in the case of some developed markets. We also show that the strength of correlations among the stocks crucially depends on the…
We investigate the financial network in the Korean stock exchange (KSE) market, using both numerical simulations and scaling arguments. We estimate the cross-correlation on the stock price exchanges of all companies listed on the the Korean stock exchange market, where all companies are fully connected via weighted links, by introducing a weighted random graph. The degree distribution and the edge density are discussed numerically from the market graph, and the statistical analysis for the degree distribution of vertices is particularly found to approximately follow the power law.
Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schrödinger equation for the stock price. Based on this theoretical framework, an example of a driven infinite quantum well is considered, in which we use a cosine distribution to simulate the state of stock price in equilibrium. After adding an external field into the Hamiltonian to analytically calculate the wave function, the distribution and the average value of the rate of return are shown.
To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack o…
Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell) or three options. However, herding effects of competing stocks and the collective dynamics of a whole market may escape our reach in the simplest models. Here I study a q-spin Potts model version of a simple Ising market model to represent the dynamics of a stock market index in a spin model. As a result, a self-organized gain-loss asymmetry in the time ser…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a stock at a certain discrete time step. The remaining cells are inactive,(0). The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Most of the stylized aspects of the financial market time series are reproduced by the…
We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlation and intra-band negative correlation between the volatility and the trading volume of stocks are derived by considering the energy band structure of the model. The validity of price limitation is then examined and abnormal phenomena of a price-limited stock market (Shanghai Stoc…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market dynamics which we study both empirically and theoretically. We demonstrate that this model replicates observed market behavior on all relevant timescales (from days to years) reasonably well. Using the model, we obtain and discuss a number of results that pose implications for current market theory and offer potential practical applications.
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenbe…
The p-adic theory of the stock market is presented. It is shown that the price dynamics is very naturally described by the adelic function. The procedure of derivation of the functional integral formulation of adelic type is derived from microscopic models using generalized supercoherent states.
In this paper we present an econophysic model for the description of shares transactions in a capital market. For introducing the fundamentals of this model we used an analogy between the electrical field produced by a system of charges and the overall of economic and financial information of the shares transactions from the stock-markets. An energetic approach of the rate variation for the shares traded on the financial markets was proposed and studied.
The Chinese stock market experienced an abrupt crash in 2015, and over one-third of its market value evaporated. Given its associations with fear and the fine resolution with respect to frequency, the illiquidity of stocks may offer a promising perspective for understanding and even signaling a market crash. In this study, by connecting stocks with illiquidity comovements, an illiquidity network is established to model the market. Compared to noncrash days, on crash days, the market is more densely connected due to heavier but more homogeneous illiquidity dependencies that facilitate abrupt co…
In this paper we present a mathematical model for collaborative filtering implementation in stock market predictions. In popular literature collaborative filtering, also known as Wisdom of Crowds, assumes that group has a greater knowledge than the individual while each individual can improve group's performance by its specific information input. There are commercially available tools for collaborative stock market predictions and patent protected web-based software solutions. Mathematics that lies behind those algorithms is not disclosed in the literature, so the presented model and algorithm…
