A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked according to their size to form a probability distribution function and finally fed in the expression of the Shannon entropy. In this work, such entropy measure is implemented on the time series of prices and volatilities of six financial markets. The analysis has been performed, on tick-by-tick data sampled every minute for six years of data from 1999 to 2004, for a broad range of moving average windows and volatility horizons. The study shows that the entropy of the volatility series depends on the individual market, while the entropy of the price series is practically a market-invariant for the six markets. Finally, a cumulative information measure - the `Market Heterogeneity Index'- is derived from the integral of the proposed entropy measure. The values of the Market Heterogeneity Index are discussed as possible tools for optimal portfolio construction and compared with those obtained by using the Sharpe ratio a traditional risk diversity measure.
Recently, to account for low-frequency market dynamics, several volatility models, employing high-frequency financial data, have been developed. However, in financial markets, we often observe that financial volatility processes depend on economic states, so they have a state heterogeneous structure. In this paper, to study state heterogeneous market dynamics based on high-frequency data, we introduce a novel volatility model based on a continuous Ito diffusion process whose intraday instantaneous volatility process evolves depending on the exogenous state variable, as well as its integrated v…
We introduce a new measure of activity of financial markets that provides a direct access to their level of endogeneity. This measure quantifies how much of price changes are due to endogenous feedback processes, as opposed to exogenous news. For this, we calibrate the self-excited conditional Poisson Hawkes model, which combines in a natural and parsimonious way exogenous influences with self-excited dynamics, to the E-mini S&P 500 futures contracts traded in the Chicago Mercantile Exchange from 1998 to 2010. We find that the level of endogeneity has increased significantly from 1998 to 2010,…
Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and n…
Financial global crisis has devastating impacts to economies since early XX century and continues to impose increasing collateral damages for governments, enterprises, and society in general. Up to now, all efforts to obtain efficient methods to predict these events have been disappointing. However, the quest for a robust estimator of the degree of the market efficiency, or even, a crisis predictor, is still one of the most studied subjects in the field. We present here an original contribution that combines Information Theory with graph concepts, to study the return rate series of 32 global t…
A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intradaily structures in the financial time-series. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the time-period between November 1997 and December 1999 and demonstrates a power of the method. In this way two significant new aspects of the DAX evolution are identified: (i) the memory effects turn out to be sizably shorter than what the standard autocor…
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 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.
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable t…
We study the cascading dynamics immediately before and immediately after 219 market shocks. We define the time of a market shock T_{c} to be the time for which the market volatility V(T_{c}) has a peak that exceeds a predetermined threshold. The cascade of high volatility "aftershocks" triggered by the "main shock" is quantitatively similar to earthquakes and solar flares, which have been described by three empirical laws --- the Omori law, the productivity law, and the Bath law. We analyze the most traded 531 stocks in U.S. markets during the two-year period 2001-2002 at the 1-minute time res…
Case Western Reserve University（凯斯西储大学）；Nankai University（南开大学）；National Institute of Health（国立卫生研究院）；Kent State University（肯特州立大学）；California State University Long Beach（加州州立大学长滩分校）
In recent years, there have been quite a few attempts to apply intelligent techniques to financial trading, i.e., constructing automatic and intelligent trading framework based on historical stock price. Due to the unpredictable, uncertainty and volatile nature of financial market, researchers have also resorted to deep learning to construct the intelligent trading framework. In this paper, we propose to use CNN as the core functionality of such framework, because it is able to learn the spatial dependency (i.e., between rows and columns) of the input data. However, different with existing dee…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility framework and prove that a parsimonious, two-scale version effectively captures the long memory as measured from the real data. Since estimating parameters in a stochastic volatility model is challenging, we introduce a robust methodology based on the Generalized Method of Moments supported by a heuristic selection of the orthogonal conditions. In addition to the v…
Cross-correlation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this end, we use the cross-recurrence plot analysis as a nonlinear method for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization. We adopt a deep learning framework for methodologically addressing the prediction of the synchronization state based on features extracted from dynamically…
We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of financial and economic markets. We study the detailed order flow on the Shenzhen Stock Exchange of China for the whole year of 2003. This enormous dataset allows us to compare (i) a closed national market (A-shares) with an international market (B-shares), (ii) individuals and institutions and (iii) real investors to random strategies with respect to timing t…
In the area of traditional physics the atomic nucleus belongs to the most complex systems. It involves essentially all elements that characterize complexity including the most distinctive one whose essence is a permanent coexistence of coherent patterns and of randomness. From a more interdisciplinary perspective, these are the financial markets that represent an extreme complexity. Here, based on the matrix formalism, we set some parallels between several characteristics of complexity in the above two systems. We, in particular, refer to the concept - historically originating from nuclear phy…
A symmetry-guided definition of time may enhance and simplify the analysis of historical series with recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns, we identify a successful protocol of time definition in Finance. The essential structure of the stochastic process underlying the series can thus be analyzed within a most parsimonious symmetry scheme in which multiscaling is reduced in the quest of a time scale additive and independent of moment-order in the distribution of returns. At the same time, duration of periods in which …
Contagion is an extremely important topic in finance. Contagion is at the core of most major financial crises, in particular the 2008 financial crisis. Although various approaches to quantifying contagion have been proposed, many of them lack a causal interpretation. We will present a new measure for contagion among individual currencies within the Foreign exchange market and show how the paths of contagion work within the Forex using causal inference. This approach will allow us to pinpoint sources of contagion and to find which currencies offer good options for diversification and which are …
In Europe, Germany is taking the lead in the switch from the conventional to renewable energy. This poses new challenges as wind and solar energy are fundamentally intermittent, weather-dependent and less predictable. It is therefore of considerable interest to investigate the evolution of price volatility in this post-transition era. There are a number of reasons, however, that makes the practical studies difficult. For instance, EPEX prices can be zero or negative. Consequently, the standard approach in financial time series analysis to switch to logarithmic measures is inapplicable. Further…
Effects connected with the world globalization affect also the financial markets. On a way towards quantifying the related characteristics we study the financial empirical correlation matrix of the 60 companies which both the Deutsche Aktienindex (DAX) and the Dow Jones (DJ) industrial average comprised during the years 1990-1999. The time-dependence of the underlying cross-correlations is monitored using a time window of 60 trading days. Our study shows that if the time-zone delays are properly accounted for the two distant markets largely merge into one. This effect is particularly visible d…
ETH Zurich（苏黎世联邦理工学院）；The Canon Institute for Global Studies（佳能全球战略研究所）；Swiss Finance Institute（瑞士金融研究院）；University of Tsukuba（筑波大学）；The University of Tokyo（东京大学）
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.) affect 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 ma…
