The endogenous dynamics of financial markets: Interaction and information dissemination

We investigate the process that different interactions between investors will prompt information to propagate along a differentiated path and construct a financial market model. As information spreads, increasingly investors are attracted to participate in trading, then the “herding effect” is magnified gradually, which will induce the topology of market network to change and the price to fluctuate. Especially, under different initial conditions or parameters, the peak and fat-tail property is produced and the obtained statistic values coincide with empirical results: the power-law exponents between the peak value of return probability distribution and the time scales range from 0.579 to 0.747, and the exponents between the accumulation distribution and the return on the tail are close to 3. Besides, the extent of volatility clustering in our produced price series is close to that of S&P 500 and locates between NASDAQ and HSI. All the results obtained here indicate that the continuous variation of the “herding effect” resulting from information propagation among interacting investors may be the origin of stylized facts of price fluctuations.     

Correlations in financial time series: established versus emerging markets

Long-time correlations in both well-developed and emerging market indexes are studied. The Hurst exponent as well as detrended fluctuations analysis (DFA) are used as technical tools. Some features that seem to be specific for developing markets are discovered and briefly discussed. Received 17 October 2000     

Open dynamic behaviour of financial markets

Open dynamic behaviour of financial markets with internal interactions between agents and with external “fields” from other systems are investigated using the approach of Grossman and Stiglitz for inefficient markets, and Keynes for interference of the market using physics of finance (referred to hereafter as phynance). The simulation results indicate that the NYSE data analyzed in Plerou, V. et al., Nature 421, 130 (2003) can be fitted by an equation of order parameter Φ and local deviation R of type: -(R+0.03) Φ+ 0.6 Φ³ + 0.02 = 0, which is shown to be in remarkable agreement with Plerou's data.     

Hitting time distributions in financial markets

We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is composed by daily price of 1071 stocks trade for the 12-year period 1987-1998, the second one is composed by high frequency data for 100 stocks for the 4-year period 1995-1998. We compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution. Specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold, we compare the probability density function (PDF) of three models, namely the geometric Brownian motion, the GARCH model and the Heston model with that obtained from real market data. We will present also some results of a generalized Heston model.     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向，与一般的数学建模不同，它是应用几何结构的模型，建立在规范场的物理思想和纤维丛的几何结构的基础上，文章介绍了规范场的物理概念思想原则，也介绍纤维丛数学概念和几何结构，然后说明规范场理论与纤维丛理论的相结合，成为与金融市场概念和运作相匹配的市场模型，举出这一模型成功引导出金融市场产品定价的Black—Scholes方程和公式。文章对象以物理学者为主，对于理论经济学、金融理论和系统科学的读者来说可略去数学推导。     

Time-reversal asymmetry in financial systems

We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and the German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents _p±$p_{\pm }$ usually vary with the strength of the large fluctuations. The large-fluctuation dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asymmetry is mainly induced by external forces. It is also the external forces which drive the financial system to a non-stationary state. Different characteristics of the Chinese and German stock markets are uncovered.     

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向,与一般的数学建模不同,它是应用几何结构的模型,建立在规范场的物理思想和纤维丛的几何结构的基础上.文章介绍了规范场的物理概念思想原则,也介绍纤维丛数学概念和几何结构,然后说明规范场理论与纤维丛理论的相结合,成为与金融市场概念和运作相匹配的市场模型,举出这一模型成功引导出金融市场产品定价的Black-Scholes方程和公式.文章对象以物理学者为主,对于理论经济学、金融理论和系统科学的读者来说可略去数学推导.     

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.     

Asymmetric conditional volatility in international stock markets

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 SP 500, FTSE 100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.     

Micro and macro benefits of random investments in financial markets

In this paper, making use of recent statistical physics techniques and models, we address the specific role of randomness in financial markets, both at the micro and the macro level. In particular, we review some recent results obtained about the effectiveness of random strategies of investment, compared with some of the most used trading strategies for forecasting the behaviour of real financial indexes. We also push forward our analysis by means of a self-organised criticality model, able to simulate financial avalanches in trading communities with different network topologies, where a Pareto-like power law behaviour of wealth spontaneously emerges. In this context, we present new findings and suggestions for policies based on the effects that random strategies can have in terms of reduction of dangerous financial extreme events, i.e. bubbles and crashes.     

On statistical properties of traded volume in financial markets

In this article we study the dependence degree of the traded volume of the Dow Jones 30 constituent equities by using a nonextensive generalised form of the Kullback-Leibler information measure. Our results show a slow decay of the dependence degree as a function of the lag. This feature is compatible with the existence of non-linearities in this type time series. In addition, we introduce a dynamical mechanism whose associated stationary probability density function (PDF) presents a good agreement with the empirical results.     

Modeling and asset allocation for financial markets based on a discrete time microstructure model

On the basis of the market microstructure theory and the continuous time stochastic volatility-style microstructure model, a discrete time stochastic volatility microstructure model with state-observability is proposed for describing the dynamics of financial markets. From the discrete time microstructure model proposed, estimates of two immeasurable state variables representing the market excess demand and liquidity respectively may be obtained. A simple trading strategy for dynamic asset allocation, based on the indirectly obtained excess demand information instead of the prediction for price, is presented. An approach to the estimation of the discrete time microstructure model using the extended Kalman filter and the maximum likelihood method is also presented. Case studies on financial market modeling and the estimated model-based asset dynamic allocation control for the JPY/USD (Japanese Yen/US Dollar) exchange rate and Japan TOPIX (TOkyo stock Price IndeX) show satisfactory modeling precision and control performance. Received 11 March 2002 / Received in final form 4 November 2002 Published online 4 February 2003 RID="a" ID="a"Currently a visiting researcher at the Institute of Statistical Mathematics, 4-6-7 Minami Azabu, Minato-ku, Tokyo 106-8569, Japan e-mail: peng@ism.ac.jp     

金融市场中幂律分布的经验和理论研究进展--经济物理学研究的一个前沿

对金融市场波动性的研究是经济物理(econophysics)的一个重要内容．物理学家们借鉴物理学研究方法对金融市场中的主要变量进行的经验研究，揭示了金融资产价格涨落及相关变量概率分布尾部的幂律渐近行为、这一性质明显有悖于传统金融学中的正态分布和试图取代它的列维分布，引起人们广泛的兴趣．文章集中介绍了关于金融资产收益率分布尾部幂律性质经验研究的主要方法和结果，以及几种相关的理论解释．     

Persistence in financial markets

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their 'starting' values. As a result, we estimate a persistence exponent for the underlying financial market to be θ_f∼0.5.     

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.     

Asymmetric Fractal Characteristics and Market Efficiency Analysis of Style Stock Indices

As a typical complex system, the stock market has attracted the attention of scholars and investors to comprehensively understand its fractal characteristics and analyze its market efficiency. Firstly, this paper proposes an asymmetric, detrended fluctuation analysis based on overlapping sliding windows (OSW-A-MFDFA). It reduces the generation of fluctuation errors, and the calculation results are more robust and reliable. The advantage of the OSW-A-MFDFA is that it not only can reveal the multifractal characteristics of time series clearly, but also can further accurately analyze the asymmetry of fractal characteristics under different trends. Secondly, this paper focuses on the variation in the width difference and height difference of the multifractal spectrum under different trends. Finally, based on multifractality, this paper proposes a comprehensive indicator MED that can be used to measure market efficiency, which is characterized by traversing all fluctuation orders. The application revealed many interesting findings in style stock indices. Style stock indices have asymmetric multifractal characteristics, and there are significant differences in the fractal spectrum of different style assets. Moreover, the market efficiency of style stock indices is time-varying, which can be reasonably explained from the perspective of the adaptive market hypothesis.     

推广的EZ模型中的普适性行为

探讨了推广EZ模型的可能性,并给出了相应的模型中人群大小分布函数的形式解.研究表明金融市场中不同大小的人群数目的交易人的数目在重新标度后将具有最广泛的普适性行为 关键词： 金融物理 人群效应 主方程     

A mini-review on econophysics:Comparative study of Chinese and western financial markets

We present a review of our recent research in econophysics, and focus on the comparative study of Chinese and western financial markets. By virtue of concepts and methods in statistical physics, we investigate the time correlations and spatial structure of financial markets based on empirical high-frequency data. We discover that the Chinese stock market shares common basic properties with the western stock markets, such as the fat-tail probability distribution of price returns, the long-range auto-correlation of volatilities, and the persistence probability of volatilities, while it exhibits very different higher-order time correlations of price returns and volatilities, spatial correlations of individual stock prices, and large-fluctuation dynamic behaviors. Furthermore, multi-agent-based models are developed to simulate the microscopic interaction and dynamic evolution of the stock markets.