The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential $U$ under the influence of the variable noise intensity, depending on the particle position $x$. Based on the empirical data the approximate estimation of the Kramers-Moyal coefficients $D_{1,2}$ allow to predicate quite definitely the behavior of the potential introduced by $D_1 = - \partial U /\partial x$ and the volatility $\sim \sqrt{D_2}$. It has been shown that the presented model describes well enough the best known empirical facts relative to the large financial crash of October 1987. \
We analyze the financial crash in 2008 for different financial markets from the point of view of log-periodic function model. In particular, we consider Dow Jones index, DAX index and Hang Seng index. We shortly discuss the possible relation of the theory of critical phenomena in physics to financial markets.
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 m…
Renowned method of log-periodic power law(LPPL) is one of the few ways that a financial market crash could be predicted. Alongside with LPPL, this paper propose a novel method of stock market crash using white box model derived from simple assumptions about the state of rational bubble. By applying this model to Dow Jones Index and Bitcoin market price data, it is shown that the model successfully predicts some major crashes of both markets, implying the high sensitivity and generalization abilities of the model.
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 discuss the statistical properties of index returns in a financial market just after a major market crash. The observed non-stationary behavior of index returns is characterized in terms of the exceedances over a given threshold. This characterization is analogous to the Omori law originally observed in geophysics. By performing numerical simulations and theoretical modelling, we show that the nonlinear behavior observed in real market crashes cannot be described by a GARCH(1,1) model. We also show that the time evolution of the Value at Risk observed just after a major crash is described b…
Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classification of the market crisis phenomena is given.
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,…
We apply two non-parametric methods to test further the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The analysis using the so-called (H,q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln(t_c-t) variable, where t_c is the time of th…
We study precursors to the global market crash that occurred on all main stock exchanges throughout the world in October 2008 about three weeks after the bankruptcy of Lehman Brothers Holdings Inc. on 15 September. We examine the collective behavior of stock returns and analyze the market mode, which is a market-wide collective mode, with constituent issues of the FTSE 100 index listed on the London Stock Exchange. Before the market crash, a sharp rise in a measure of the collective behavior was observed. It was shown to be associated with news including the words "financial crisis." They did …
During any unique crisis, panic sell-off leads to a massive stock market crash that may continue for more than a day, termed as mainshock. The effect of a mainshock in the form of aftershocks can be felt throughout the recovery phase of stock price. As the market remains in stress during recovery, any small perturbation leads to a relatively smaller aftershock. The duration of the recovery phase has been estimated using structural break analysis. We have carried out statistical analyses of the 1987 stock market crash, 2008 financial crisis and 2020 COVID-19 pandemic considering the actual cras…
We employed the log-periodic power law singularity (LPPLS) methodology to systematically investigate the 2020 stock market crash in the U.S. equities sectors with different levels of total market capitalizations through four major U.S. stock market indexes, including the Wilshire 5000 Total Market index, the S&P 500 index, the S&P MidCap 400 index, and the Russell 2000 index, representing the stocks overall, the large capitalization stocks, the middle capitalization stocks and the small capitalization stocks, respectively. During the 2020 U.S. stock market crash, all four indexes lost more tha…
A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condition. This paper examines these claims and the robustness of the LPPL for capturing large falls in the Hang Seng stock market index, over a 30-year period, including the current global downturn. We identify 11 crashes on the Hang Seng market over the period 1970 to 2008. The fitte…
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power law relaxation decay of its typical scale. Our empirical observati…
We select the $n$ stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the $k$ trading days of our database from the stock price time series. We study the ensemble return distribution for each trading day and we find that the symmetry properties of the ensemble return distribution drastically change in crash and rally days of the market. We compare these empirical results with numerical simulations based on the single-index model and we conclude that this model is unable to explain the behavior of the market in extreme days.
Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "anti-bubbles" appear after a crash, when the prices decreases. Here, we propose the third type of log-periodic oscillations, where a exogenous crash initializes a log-periodic behavior of market, and the market is growing up. Such behavior has been identified on Polish stock market…
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…
We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two transitions of the topology of a complex network representing FSE were found. First transition is from a hierarchical scale-free MST representing the stock market before the recent worldwide financial crash, to a superstar-like MST decorated by a scale-free hierarchy of trees repre…
A major impact of globalization has been the information flow across the financial markets rendering them vulnerable to financial contagion. Research has focused on network analysis techniques to understand the extent and nature of such information flow. It is now an established fact that a stock market crash in one country can have a serious impact on other markets across the globe. It follows that such crashes or critical regimes will affect the network dynamics of the global financial markets. In this paper, we use sequential change point detection in dynamic networks to detect changes in t…
We study the information dynamics between the largest Bitcoin exchange markets during the bubble in 2017-2018. By analysing high-frequency market-microstructure observables with different information theoretic measures for dynamical systems, we find temporal changes in information sharing across markets. In particular, we study the time-varying components of predictability, memory, and synchronous coupling, measured by transfer entropy, active information storage, and multi-information. By comparing these empirical findings with several models we argue that some results could relate to intra-m…
In this empirical paper we show that in the months following a crash there is a distinct connection between the fall of stock prices and the increase in the range of interest rates for a sample of bonds. This variable, which is often referred to as the interest rate spread variable, can be considered as a statistical measure for the disparity in lenders' opinions about the future; in other words, it provides an operational definition of the uncertainty faced by economic agents. The observation that there is a strong negative correlation between stock prices and the spread variable relies on th…
The dynamical behavior of the currency exchange rate after its large-scale catastrophe is discussed through a case study of the rate of Russian rubles to US dollars after its crash in 2014. It is shown that, similarly to the case of the stock market crash, the relaxation is characterized by a power law, which is in analogy with the Omori-Utsu law for earthquake aftershocks. The waiting-time distribution is found to also obey a power law. Furthermore, the event-event correlation is discussed, and the aging phenomenon and scaling property are observed. Comments are made on (non-)Markovianity of …
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…
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,…
We perform an extended analysis of the distribution of drawdowns in the two leading exchange markets (US dollar against the Deutsmark and against the Yen), in the major world stock markets, in the U.S. and Japanese bond market and in the gold market, by introducing the concept of ``coarse-grained drawdowns,'' which allows for a certain degree of fuzziness in the definition of cumulative losses and improves on the statistics of our previous results on the existence of ``outliers'' or ``kings.'' Then, for each identified outlier, we check whether log-periodic power law signatures (LPPS) are pres…
Over the last two decades, financial systems have been studied and analysed from the perspective of complex networks, where the nodes and edges in the network represent the various financial components and the strengths of correlations between them. Here, we adopt a similar network-based approach to analyse the daily closing prices of 69 global financial market indices across 65 countries over a period of 2000-2014. We study the correlations among the indices by constructing threshold networks superimposed over minimum spanning trees at different time frames. We investigate the effect of criti…
By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles. It embodies a positive feedback loop of higher return anticipations competin…
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\rq values. As a result, we estimate a persistence exponent for the underlying financial market to be $θ_f\sim 0.5$.
The aim of this study is to investigate quantitatively whether share prices deviated from company fundamentals in the stock market crash of 2008. For this purpose, we use a large database containing the balance sheets and share prices of 7,796 worldwide companies for the period 2004 through 2013. We develop a panel regression model using three financial indicators--dividends per share, cash flow per share, and book value per share--as explanatory variables for share price. We then estimate individual company fundamentals for each year by removing the time fixed effects from the two-way fixed e…
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…
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…
We study the phase transition of dynamical herd behaviors for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior with three different values of the scaling exponent 3.11 (one time lag $τ$ = 1 minute), 2.81 (30 minutes), and 2.29 (1 hour). The crash regime in which the probabilty density increases with the increasing return appears in the case of $τ$ < 30 minutes, while it occurs no financial crash at $τ$ > 30 minutes. it is especially obtained that our dynamical herd behavior exhibits the p…
Coronavirus (COVID-19) creates fear and uncertainty, hitting the global economy and amplifying the financial markets volatility. The oil price reaction to COVID-19 was gradually accommodated until March 09, 2020, when, 49 days after the release of the first coronavirus monitoring report by the World Health Organization (WHO), Saudi Arabia floods the market with oil. As a result, international prices drop with more than 20% in one single day. Against this background, the purpose of this paper is to investigate the impact of COVID-19 numbers on crude oil prices, while controlling for the impact …
Several authors have noticed the signature of log-periodic oscillations prior to large stock market crashes [cond-mat/9509033, cond-mat/9510036, Vandewalle et al 1998]. Unfortunately good fits of the corresponding equation to stock market prices are also observed in quiet times. To refine the method several approaches have been suggested: 1) Logarithmic Divergence: Regard the limit where the critical exponent βconverges to 0. 2) Universality: Define typical ranges for the free parameters, by observing the best fit for historic crashes. We suggest a new approach. From the observation that the h…
We investigate the local fractal properties of the financial time series based on the evolution of the Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. Calculating the local Hurst exponent for the WIG time series we find an interesting dependence between the behavior of the local fractal properties of the WIG time series and the crashes appearance on the financial market.
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 perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 stocks listed on the Shanghai and Shenzhen stock exchanges. Both raw correlation matrix and partial correlation matrix with respect to the market index in two time periods of one year are investigated. We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007 and the average partial correlation is significantly weaker than the average correlation in each period. Acc…
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 …
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…
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 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.
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…
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…
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…
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 …
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…
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…
A new approach to the understanding of complex behavior of financial markets index using tools from thermodynamics and statistical physics is developed. Physical complexity, a magnitude rooted in Kolmogorov-Chaitin theory is applied to binary sequences built up from real time series of financial markets indexes. The study is based on NASDAQ and Mexican IPC data. Different behaviors of this magnitude are shown when applied to the intervals of series placed before crashes and to intervals when no financial turbulence is observed. The connection between our results and The Efficient Market Hypoth…
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.
