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.     

Hierarchical structure in financial markets

I find a hierarchical arrangement of stocks traded in a financial market by investigating the daily time series of the logarithm of stock price. The topological space is a subdominant ultrametric space associated with a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides a meaningful economic taxonomy. Received 24 March 1999 and Received in final form 28 June 1999     

Activity autocorrelation in financial markets

We study the activity of financial markets, i.e., the number of transactions per unit of time. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power-law which ultimately recovers an exponential behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.Received: 15 March 2004, Published online: 8 June 2004PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 05.45.Tp Time series analysis - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

Treatment of kurtosis in financial markets

Since Mandelbrot (1963) [2] highlighted the fact that data on the yield of financial assets exhibit leptokurtosis, different distributions have been presented as alternatives to the normal distribution. So far little consideration has been given to the capacity that these distributions have to recover the kurtosis of the sample data. Our work aims to present distributions which, given the broad range of their kurtosis, have the capacity to perform adjustment on many occasions where other distributions fail, while also being capable of recovering the peakedness of the empirical data. Another key characteristic of these distributions is that they are defined within a bounded domain in the same way as the sample data. An empirical application of these distributions is presented within the financial field by using daily returns.     

Persistence and financial markets

The persistence phenomenon is studied in a financial context by using a novel mapping of the time evolution of the values of shares in a portfolio onto Ising spins. The method is applied to historical data from the London Financial Times Stock Exchange 100 index (FTSE 100) over an arbitrarily chosen period. By following the time dependence of the spins, we find evidence for a 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 ≈0.5. Preliminary results from computer simulations on persistence in the economic dynamics of a toy model appear to reproduce the behaviour observed in real markets.     

Waiting time distributions in financial markets

We study waiting time distributions for data representing two completely different financial markets that have dramatically different characteristics. The first are data for the Irish market during the 19th century over the period 1850 to 1854. A total of 10 stocks out of a database of 60 are examined. The second database is for Japanese yen currency fluctuations during the latter part of the 20th century (1989-1992). The Irish stock activity was recorded on a daily basis and activity was characterised by waiting times that varied from one day to a few months. The Japanese yen data was recorded every minute over 24 hour periods and the waiting times varied from a minute to a an hour or so. For both data sets, the waiting time distributions exhibit power law tails. The results for Irish daily data can be easily interpreted using the model of a continuous time random walk first proposed by Montroll and applied recently to some financial data by Mainardi, Scalas and colleagues. Yen data show a quite different behaviour. For large waiting times, the Irish data exhibit a cut off; the Yen data exhibit two humps that could arise as result of major trading centres in the World. Received 31 December 2001     

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.     

Average cross-responses in correlated financial markets

There are non-vanishing price responses across different stocks in correlated financial markets, reflecting non-Markovian features. We further study this issue by performing different averages, which identify active and passive cross-responses. The two average cross-responses show different characteristic dependences on the time lag. The passive cross-response exhibits a shorter response period with sizeable volatilities, while the corresponding period for the active cross-response is longer. The average cross-responses for a given stock are evaluated either with respect to the whole market or to different sectors. Using the response strength, the influences of individual stocks are identified and discussed. Moreover, the various cross-responses as well as the average cross-responses are compared with the self-responses. In contrast to the short-memory trade sign cross-correlations for each pair of stocks, the sign cross-correlations averaged over different pairs of stocks show long memory.     

The seismography of crashes in financial markets

This Letter investigates the dynamics of stocks in the S&P500 for the last 33 years, considering the population of all companies present in the index for the whole period. Using a stochastic geometry technique and defining a robust index of the dynamics of the market structure, which is able to provide information about the intensity of the crises, the Letter proposes a seismographic classification of the crashes that occurred during the period. The index is used in order to investigate and to classify the impact of the thirteen crashes between July 1973 and March 2006 and to discuss the available evidence of change of structure after the fin de siècle.     

Probability of large movements in financial markets

Based on empirical financial time series, we show that the “silence-breaking” probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going low-variability period. Such a scaling law has been previously predicted theoretically [R. Kitt, J. Kalda, Physica A 353 (2005) 480], assuming that the length-distribution of the low-variability periods follows a multi-scaling power law.     

Conditional dynamics driving financial markets

We revisit the problem of daily correlations in speculative prices and report empirical evidences on the existence of what we term a conditional or dual dynamics driving the evolution of financial assets. This dynamics is detected in several markets around the world and for different historical periods. In particular, we have analyzed the DJIA database from 1900 to 2002 as well as 65 companies trading in the LIFFE market of futures and 12 of the major European and American treasury bonds. In all cases, we find a twofold dynamics driving the financial evolution depending on whether the previous price went up or down. We conjecture that this effect is universal and intrinsic to all markets.Received: 14 April 2004, Published online: 31 August 2004PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 05.45.Tp Time series analysis - 87.23.Ge Dynamics of social systems     

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.     

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.     

Asymmetric and symmetric meta-correlations in financial markets

In financial markets, the relation between fluctuations of stock prices and trading behaviors is complex. It is intriguing to quantify this kind of meta-correlation between market fluctuations and the synchronous behaviors. We refine the theoretical index leverage model proposed by Reigneron et al., to exactly quantify the meta-correlation under various levels of price fluctuations [Reigneron P A, Allez R and Bouchaud J P 2011 Physica A 390 3026]. The characteristics of meta-correlations in times of market losses, are found to be significantly different in Chinese and American financial markets. In addition,unlike the asymmetric results at the daily scale, the correlation behaviors are found to be symmetric at the high-frequency scale.     

Spurious trend switching phenomena in financial markets

Transport of overdamped Brownian particles in deformable potentials is investigated in the presence of asymmetrically unbiased fluctuations. It is found that the deformation of the potential can strongly affect the directed transport. For small noise strength, the current is not always monotonic function of deformable parameter. For large noise strength, there exists a value of deformable parameter at which the current takes its maximum. Therefore, it is possible to obtain the optimal transport by changing the deformation of the potential.     

Correlation of financial markets in times of crisis

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 financial market crises that occurred in the years 1987 (Black Monday), 1998 (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 decades.     

Understanding the source of multifractality in financial markets

In this paper, we use the generalized Hurst exponent approach to study the multi-scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multi-scaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal model, autoregressive fractionally integrated moving average processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality.     

Dynamical mechanism of two-phase phenomena in financial markets

Two-phase behavior of the Korean treasury bond (KTB) futures in the Korean exchange market is investigated in this study. To show that the two-phase phenomena are due to heavy-tailed behavior of distribution of price returns, actual data from the KTB futures market with shuffled data and a generated time series are examined according to the Brownian process. In addition, we study the correlation inherent in the KTB futures and its Brownian walk, describing the extent to which the volatility clustering plays a crucial role in equilibrium and nonequilibrium states of financial markets. It is shown that the two-phase behavior essentially results from heavy-tailed behavior of the distribution of price returns. This two-phase behavior does not appear to be relevant to volatility clustering.     

Diagnosis and prediction of rebounds in financial markets

We introduce the concept of “negative bubbles” as the mirror (but not necessarily exactly symmetric) image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a hazard rate describing the collective buying pressure of noise traders. The price fall occurring during a transient negative bubble can be interpreted as an effective random down payment that rational agents accept to pay in the hope of profiting from the expected occurrence of a possible rally. We validate the model by showing that it has significant predictive power in identifying the times of major market rebounds. This result is obtained by using a general pattern recognition method that combines the information obtained at multiple times from a dynamical calibration of the JLS model. Error diagrams, Bayesian inference and trading strategies suggest that one can extract genuine information and obtain real skill from the calibration of negative bubbles with the JLS model. We conclude that negative bubbles are in general predictably associated with large rebounds or rallies, which are the mirror images of the crashes terminating standard bubbles.     

The timing of information transmission in financial markets

This article shows turbulent behavior in a series of financial indexes assuming that they follow a cascade process of the same type as do turbulent fluids. With such a model, the energy flux between the eddies that emerge in the fluid is analogous to the financial information flux over the course of time. The results obtained confirm the variability of variation of the indexes for the considered time scale (the turbulent intermittency typical for fluids), and they also confirm that when we descend along the cascade, that is to say, when we consider smaller time intervals, the rate at which the hypothetical eddies of information dissipate becomes greater than the rate at which the information is transmitted. This fact can explain the cyclical nature of crises: ultimately, financial events have a memory of the past. Besides, the NASDAQ singular behavior regarding the number of jumps, the degree of intermittency of the turbulence and the life time of the hypothetical eddies has been analysed.