The paper has gone through considerable revisions after referees' comments. The major changes are, The old introduction has been split into Section 1: Introduction and Section 2: A brief review of the Theory. The Results section now has 4 subsections. Section 5 (Conclusions) is reworded but the conclusions remain the same. Some additional references have been added. 29 pages. 11 Figures
The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random walk model. In this work, a good fit to a Tsallis q-Gaussian distribution is obtained for the distributions of all the returns using the method of Maximum Likelihood Estimate. For all the regions of data considered, the values of the scaling parameter q, estimated from one day returns, lie in the range 1.4 to 1.65. The estimated inverse mean square deviations (beta) show a power law behavior in time with exponent values between -0.91 and -1.1 indicating normal to mildly subdiffusive behavior. Quite often, the dynamics of market return distributions is modelled by a Fokker-Plank (FP) equation either with a linear drift and a nonlinear diffusion term or with just a nonlinear diffusion term. Both of these cases support a q-Gaussian distribution as a solution. The distributions obtained from current estimated parameters are compared with the solutions of the FP equations. For negligible drift term, the inverse mean square deviations (betaFP) from the FP model follow a power law with exponent values between -1.25 and -1.48 indicating superdiffusion. When the drift term is non-negligible, the corresponding betaFP do not follow a power law and become stationary after certain characteristic times that depend on the values of the drift parameter and q. Neither of these behaviors is supported by the results of the empirical fit.
The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low frequency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited predictive power in this phenomenological approach and present a stochastic model, based on the scaling symmetry of financial a…
We investigate the financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize the individuals in a financial market by their trading strategy, namely noise traders and fundamentalists. The opinion of a local majority compels the market exchanging behavior of noise traders, whereas the global behavior of the market influences the fundamentalist agents' decisions. We introduce a noise parameter $q$ to represent a level of anxiety and perceived uncertainty regarding the market behavior, enabling the possibility for an adrift financial a…
Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigen-centralities of different stocks in the cross-correlation matrix, to extract information about the disor…
The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and discussed.
Liberalization of electricity markets has increasingly created the need for understanding the volatility and correlation structure between electricity and financial markets. This work reveals the existence of structural changes in correlation patterns among these two markets and links the changes to both fundamentals and regulatory conditions prevailing in the markets, as well as the current European financial crisis. We apply a Dynamic Conditional Correlation (DCC) GARCH model to a set of market s fundamental variables and Greece s financial market and microeconomic indexes to study their int…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure. We identify the dominating variable and extract its explicit stochastic model. This allows us to establish a connection between its time evolution and known historical events on the market. We discuss the dynamics, the stability and the hierarchy of the recently proposed quasi-stationary market states.
Using the eigenvalues and eigenvectors of correlations matrices of some of the main financial market indices in the world, we show that high volatility of markets is directly linked with strong correlations between them. This means that markets tend to behave as one during great crashes. In order to do so, we investigate several financial market crises that occurred in the years 1987 (Black Monday), 1989 (Russian crisis), 2001 (Burst of the dot-com bubble and September 11), and 2008 (Subprime Mortgage Crisis), which mark some of the largest downturns of financial markets in the last three deca…
The financial market trend forecasting method is emerging as a hot topic in financial markets today. Many challenges still currently remain, and various researches related thereto have been actively conducted. Especially, recent research of neural network-based financial market trend prediction has attracted much attention. However, previous researches do not deal with the financial market forecasting method based on LSTM which has good performance in time series data. There is also a lack of comparative analysis in the performance of neural network-based prediction techniques and traditional …
We demonstrate that future market correlation structure can be predicted with high out-of-sample accuracy using a multiplex network approach that combines information from social media and financial data. Market structure is measured by quantifying the co-movement of asset prices returns, while social structure is measured as the co-movement of social media opinion on those same assets. Predictions are obtained with a simple model that uses link persistence and link formation by triadic closure across both financial and social media layers. Results demonstrate that the proposed model can predi…
The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous scaling exponents deviated from Kolmogorov monofractal scaling of the velocity fluctuation in fluid turbulence, is applied to study and quantify the hierarchical structure of stock price fluctuations in financial markets. We therefore observed certain interesting results: (i) The hierarchical structure related to multifractal scaling generally presents in all the…
The cohomology theory for financial market can allow us to deform Kolmogorov space of time series data over time period with the explicit definition of eight market states in grand unified theory. The anti-de Sitter space induced from a coupling behavior field among traders in case of a financial market crash acts like gravitational field in financial market spacetime. Under this hybrid mathematical superstructure, we redefine a behavior matrix by using Pauli matrix and modified Wilson loop for time series data. We use it to detect the 2008 financial market crash by using a degree of cohomolog…
We compare correlations and coherent structures in nuclei and financial markets. In the nuclear physics part we review giant resonances which can be interpreted as a coherent structure embedded in chaos. With similar methods we investigate the financial empirical correlation matrix of the DAX and Dow Jones. We will show, that if the time-zone delay is properly accounted for, the two distinct markets largely merge into one. This is reflected by the largest eigenvalue that develops a gap relative to the remaining, chaotic eigenvalues. By extending investigations of the specific character of fina…
Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for different thresholds and diverse periods of time, so that it is then possible to analyze how clusters are formed according to correlations among indices and how they evolve in time, particularly during times of financial crises. Further analysis is made on the eigenvectors corresponding to the second highest eigenvalues of the correlation matrices, revealing a structure peculiar to markets that operate in different time zones.
Motivated by recent financial crises significant research efforts have been put into studying contagion effects and herding behaviour in financial markets. Much less has been said about influence of financial news on financial markets. We propose a novel measure of collective behaviour in financial news on the Web, News Cohesiveness Index (NCI), and show that it can be used as a systemic risk indicator. We evaluate the NCI on financial documents from large Web news sources on a daily basis from October 2011 to July 2013 and analyse the interplay between financial markets and financially relate…
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time intervals. Long-range time-correlations are revealed, and are found to persist up to a month-order magnitude of the price return time interval. Multifractal nature is investigated by a multifractal detrended fluctuation analysis.
Using data from 92 indices of stock exchanges worldwide, I analize the cluster formation and evolution from 2007 to 2010, which includes the Subprime Mortgage Crisis of 2008, using asset graphs based on distance thresholds. I also study the survivability of connections and of clusters through time and the influence of noise in centrality measures applied to the networks of financial indices.
We solved a stylized fact on a long memory process of volatility cluster phenomena by using Minkowski metric for GARCH(1,1) under assumption that price and time can not be separated. We provide a Yang-Mills equation in financial market and anomaly on superspace of time series data as a consequence of the proof from the general relativity theory. We used an original idea in Minkowski spacetime embedded in Kolmogorov space in time series data with behavior of traders.The result of this work is equivalent to the dark volatility or the hidden risk fear field induced by the interaction of the behav…
We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statis…
Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the validity of a multiplicative hierarchical random cascade model through an empirical study using financial data. Although the intermittency and multifractality of the time series are verified, random multiplicative factors linking successive hierarchical layers show strongly negative correlation. We extend the multiplicative model to incorporate an additional s…
As more and more data being created every day, all of it can help take better decisions with data analysis. It is not different from data generated in financial markets. Here we examine the process of how the global economy is affected by the market sentiment influenced by the micro-blogging data (tweets) of American President Donald Trump. The news feed is gathered from The Guardian and Bloomberg from the period between December 2016 and October 2019, which are used to further identify the potential tweets that influenced the markets as measured by changes in equity indices.
We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis.
We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hypothesis considers financial markets as com- plex systems consisting of many heterogenous agents, which are distinguishable mainly with respect to their investment horizon. In the paper, several novel measures of trading activity at different investment horizons are introduced th…
This paper explores when the financial market lost the price formation function in prewar Japan in the sense of Fama's (1970) semi-strong form market efficiency using a new dataset. We particularly focus on the relationship between the prewar Japanese financial market and several government policy interventions to explore whether the semi-strong form market efficiency evolves over time. To capture the long-run impact of government policy interventions against the markets, we measure the time-varying joint degree of market efficiency and the time-varying impulse responses based on Ito et al.'s …
In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated.
We contrast Arbitrage Pricing Theory (APT), the theoretical basis for the development of financial instruments, with a dynamical picture of an interacting market, in a simple setting. The proliferation of financial instruments apparently provides more means for risk diversification, making the market more efficient and complete. In the simple market of interacting traders discussed here, the proliferation of financial instruments erodes systemic stability and it drives the market to a critical state characterized by large susceptibility, strong fluctuations and enhanced correlations among risk…
Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believed to be critical by analogy to physical systems but few statistically founded evidence have been given. Through a data-based methodology and comparison to simulations inspired by statistical physics of complex systems, we show that the Dow Jones and indices sets are not rigorousl…
To investigate the universal structure of interactions in financial dynamics, we analyze the cross-correlation matrix C of price returns of the Chinese stock market, in comparison with those of the American and Indian stock markets. As an important emerging market, the Chinese market exhibits much stronger correlations than the developed markets. In the Chinese market, the interactions between the stocks in a same business sector are weak, while extra interactions in unusual sectors are detected. Using a variation of the two-factor model, we simulate the interactions in financial markets.
I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect competition, where full information is available to all market participants, the equilibrium develops a marked vulnerability (or susceptibility) to market imperfections, as markets approach completeness and transaction costs vanish. The decrease in transaction costs arises because financial institutions exploit trading instruments to hedge other instruments. This ent…
We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with the exogenous noise. The interplay between the endogenous dynamics of agents and the exogenous noise is the primary mechanism responsible for the observed long-range dependence and statistical properties of high volatility return intervals. By exogenous noise we mean information flow or/and order flow fluctuations. Numerical results based on the proposed model reveal that the exogenous fluctuations have to be considered as indispensable part of comprehensive modeling of the fin…
We investigate the problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market data. We show that Laplacian constraints have meaningful physical interpretations related to the market index factor and to the conditional correlations between stocks. Those interpretations lead to a set of guidelines that users should be aware of when estimating graphs in financial markets. In addition, we propose algorithms to learn undirected graphs that account for stylized facts and tasks intrinsic to financial data such as non-stationarity …
A new space-time model for interacting agents on the financial market is presented. It is a combination of the Curie-Weiss model and a space-time model introduced by Järpe 2005. Properties of the model are derived with focus on the critical temperature and magnetization. It turns out that the Hamiltonian is a sufficient statistic for the temperature parameter and thus statistical inference about this parameter can be performed. Thus e.g. statements about how far the current financial situation is from a financial crisis can be made, and financial trading stability be monitored for detection of…
Asymptotic arbitrage and numéraire portfolios in large financial markets
本文讨论了大金融市场的概念和Yu. M. Kabanov和D.O.克拉姆科夫我们证明了一个大市场的套利性质完全由与小市场相关的数字投资组合序列的渐近行为决定。所得到的标准可以表示在邻接，整个分离和Hellinger积分，提供这些概念被扩展到子概率测度。作为例子，我们考虑有限概率空间上的市场模型，半鞅和扩散模型。最后研究了一个离散时间无限时域对数正态股票市场模型。
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 …
We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account how past events influence the occurrence of future events. By analyzing the empirical data for 15 different financial assets, we show that the formalism of the Hawkes process used for earthquakes can successfully model the PDF of interevent times between successive market losses.
In this paper, we investigate the effect of the U.S.--China trade war on stock markets from a financial contagion perspective, based on high-frequency financial data. Specifically, to account for risk contagion between the U.S. and China stock markets, we develop a novel jump-diffusion process. For example, we consider three channels for volatility contagion--such as integrated volatility, positive jump variation, and negative jump variation--and each stock market is able to affect the other stock market as an overnight risk factor. We develop a quasi-maximum likelihood estimator for model par…
