This paper investigates the dynamics of stocks in the S&P500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose, which is a robust index of the dynamics of the market structure and provides information on the intensity and the sectoral impact of the crises. With this measure, we analyze the effects of some extreme phenomena on the geometry of the market. Nine crashes between 1987 and 2001 are compared by looking at the way they modify the shape of the manifold that describes the S&P500 market space. These crises are identified as (a) structural, (b) general and (c) local.
The paper is devoted to elaboration of a novel specific indicator based on the modified Holder exponents. This indicator has been used for forecasting critical points of financial time series and crashes of the USA stock market. The proposed approach is based on the hypothesis, which claims that before market critical points occur the dynamics of financial time series radically changes, namely time series become smoother. The approach has been tested on the stylized data and real USA stock market data. It has been shown that it is possible to forecast such critical points of financial time ser…
We find prominent similarities in the features of the time series for the overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.
We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A change in market state is identified as a change in the first PC coefficients. Some indices do not show significant change of PCs in market state during crises. The indices exposed to the invested capitals in the stock markets are at the minimum level of risk. Using the first two…
In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period of the forming of the internet bubble in Japn, and its bursting in the Japanese stock market. We found that the tail of the complementary cumulative distribution function of the ensemble of stock prices in the high value of the price is well described by a…
This review is a partial synthesis of the book ``Why stock market crash'' (Princeton University Press, January 2003), which presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. The study of the frequency distribution of drawdowns, or runs of successive losses shows that large financial crashes are ``outliers'': they form a class of their own as can be seen from their statistical signatures. If large financial crashes are ``outliers'', they are special and thus require a special explanation,…
In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention on the relative price defined as $ X(t) = S(t)/S(0) $, where $ S(0) $ is the initial price. We selected approximately 3200 stocks traded on the Japanese Stock Exchange and formed a statistical ensemble of daily relative prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period in which the {\it internet Bubble} formed and {\it crashes} in the Japanese stock market. We found that the upper tail of the complementar…
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 …
A financial system contains many elements networked by their relationships. Extensive works show that topological structure of the network stores rich information on evolutionary behaviors of the system such as early warning signals of collapses and/or crises. Existing works focus mainly on the network structure within a single stock market, while a collapse/crisis occurs in a macro-scale covering several or even all markets in the world. This mismatch of scale leads to unacceptable noise to the topological structure, and lack of information stored in relationships between different markets. I…
We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.
Pearson correlation and mutual information based complex networks of the day-to-day returns of US S&P500 stocks between 1985 and 2015 have been constructed in order to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations …
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…
We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the …
The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the 'rules of the game' in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the …
We introduce a mathematical criterion defining the bubbles or the crashes in financial market price fluctuations by considering exponential fitting of the given data. By applying this criterion we can automatically extract the periods in which bubbles and crashes are identified. From stock market data of so-called the Internet bubbles it is found that the characteristic length of bubble period is about 100 days.
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…
We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of aftershocks of a given size with time t by a power law with exponent close to 1. A shock followed by such a power law decay in the rate is here called Omori process. Studying several aftercrash time series, we show that the Omori law holds not only after significant market crashes, bu…
The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial market as an example of a complex system, and do a comparative analyses of two stock markets - the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation structure patterns of short time-epochs for a 32-year period (1985-2016). We identify "market states" as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the ev…
The financial market is a complex dynamical system composed of a large variety of intricate relationships between several entities, such as banks, corporations and institutions. At the heart of the system lies the stock exchange mechanism, which establishes a time-evolving network of trades among companies and individuals. Such network can be inferred through correlations between time series of companies stock prices, allowing the overall system to be characterized by techniques borrowed from network science. Here we study the presence of communities in the inferred stock market network, and s…
Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets from 1985 onward, and study the evolution of the cross-correlation structures of stock return matrices and their eigenspectra over different short time-intervals or "epochs". A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the e…
The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have often been represented as networks whose interacting pairs of nodes are stocks, connected by edges that signify the correlation strengths. However, we often have interactions that occur in groups of three or more nodes, and these cannot be described simply by pairwise interactions but we also need to take the relations between these interactions into account…
Econophysics is a science in its infancy, born about ten years ago at this time of writing, at the crossing roads of physics, mathematics, computing and of course economics and finance. It also covers human sciences, because all economics is ultimately driven by human decision. From this human factor, econophysics has no hope to achieve the status of an exact science, but it is interesting to discover what can be achieved, discovering potential limits and trying try to push further away these limits. A few data analysis techniques are described with emphasis on the Detrended Fluctuation Analys…
The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find that the occurrence rate of aftershocks with the magnitude exceeding a given threshold for both daily volatility (constructed using 1-minute data) and minutely volatility (using intra-minute data) decays as a power law. The power-law relaxation exponent increases with the volatilit…
We argue that the present crisis and stalling economy continuing since 2007 are rooted in the delusionary belief in policies based on a "perpetual money machine" type of thinking. We document strong evidence that, since the early 1980s, consumption has been increasingly funded by smaller savings, booming financial profits, wealth extracted from house price appreciation and explosive debt. This is in stark contrast with the productivity-fueled growth that was seen in the 1950s and 1960s. This transition, starting in the early 1980s, was further supported by a climate of deregulation and a massi…
The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang (Some new results on the Levy, Levy and Solomon microscopic stock market model, Physica A, 291(1-4)) have shown that the model exhibits finite-size effects. In this study we extend existing work in several directions. First, we show simulations which reveal finite-size effects of the model. Secondly, we shed li…
We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger tha…
The time dependence of the recently introduced minimum spanning tree description of correlations between stocks, called the ``asset tree'' have been studied to reflect the economic taxonomy. The nodes of the tree are identified with stocks and the distance between them is a unique function of the corresponding element of the correlation matrix. By using the concept of a central vertex, chosen as the most strongly connected node of the tree, an important characteristic is defined by the mean occupation layer (MOL). During crashes the strong global correlation in the market manifests itself by a…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed. A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular. An effective meth…
A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes, and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective phenomena where discrete scale invariance plays an important role. Here I investigate two distinct approaches towards the general problem of how to detect log-periodic oscillations in arbitrary time series without prior knowledge of the location of the moveable singularity. I firs…
