Anirban Chakraborti
We present an outlook of the studies on correlations in the price timeseries of stocks, discussing the construction and applications of "asset tree". The topic discussed here should illustrate how the complex economic system (financial market) enrichens the list of existing dynamical systems that physicists have been studying for long.
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This paper analyzes the quantitative relations between stock prices and quantities of tradable stock shares in Chinese stock markets at six time points by means of Exploratory Data Analysis (EDA) method. It is found the resulting formulae have the same structure but different parameters. This paper also uses these relationships in order to analyse the feasibility of policies for Chinese Government to sell the state-owned shares in Chinese stock markets.
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of volatility dynamics of denoised series are noticeably different from those of the raw data and the noise.
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives a qualitative agreement with real data.
The NYSE and NASDAQ stock markets have very different structures and there is continuing controversy over whether differences in stock price behaviour are due to market structure or company characteristics. As the influence of market structure on stock prices may be obscured by exogenous factors such as demand and supply, we hypothesize that modulation of the flow of transactions due to market operations may carry a stronger imprint of the internal market mechanism. We analyse times between consecutive transactions (ITT) for NYSE and NASDAQ stocks, and we relate the dynamical properties of the…
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as general stock price formuli in closed forms which are able to generate a variety of possible price movements in time. A kind of mechanics is submitted to cover the price movements in terms of classical concepts. Where utilizing stock mechanics to grow the portfolios in real markets is also proven.
We investigate the strength and the direction of information transfer in the U.S. stock market between the composite stock price index of stock market and prices of individual stocks using the transfer entropy. Through the directionality of the information transfer, we find that individual stocks are influenced by the index of the market.
We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the linear approximation of the drift parameter in Langevin equation estimated from the financial time series. By choosing suitable weighted factor for the linear approximation, the relation between the dynamical effect of restoring force and the autocorrelation of the financial time series is deduced. We especially analyze the daily log-returns of S$&$P 500 index fr…
In this paper we quantitatively investigate the statistical properties of an ensemble of {\it stock prices}. We selected 1200 stocks traded in the Tokyo Stock Exchange and formed a statistical ensemble of daily stock prices for each trading day in the 5 year period from January 4, 1988 to December 30, 1992. We found that the tail of the complementary cumulative distribution function of the ensembles is accurately described by a power-law distribution with an exponent that moves in the range of $ 1.7 < α< 2.2 $.
We use insight from a model of earth tectonic plate movement to obtain a new understanding of the build up and release of stress in the price dynamics of the worlds stock exchanges. Nonlinearity enters the model due to a behavioral attribute of humans reacting disproportionately to big changes. This nonlinear response allows us to classify price movements of a given stock index as either being generated due to specific economic news for the country in question, or by the ensemble of the worlds stock exchanges reacting together like a complex system. Similar in structure to the Capital Asset Pr…
In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, whereas news tend on average to be followed by lower volatility levels. The shape of the volatility relaxation is also markedly different in the two cases. Finally, we provide direct evidence that large tra…
We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price according to a power-law, and it isn't randomly drawn from the distribution, but has a strong correlation with the size of cumulative unexecuted limit orders on the price. It was also found that the limit price, on the coarse-grained price scale, tends to gather around the price whi…
We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlation and intra-band negative correlation between the volatility and the trading volume of stocks are derived by considering the energy band structure of the model. The validity of price limitation is then examined and abnormal phenomena of a price-limited stock market (Shanghai Stoc…
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.
To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack o…
This article summarizes recent research in financial economics about why information, such as earnings announcements, moves stock prices. The article does not presume any prior exposure to finance beyond what you might read in newspapers.
Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a minority-majority model and indeed it is capable of reconstructing the prevailing traders' strategies in a given time interval. Then we also analyze real (NYSE) stock-prices dynamics and it is possible to derive an indication for the the ``sentiment'' of the market for time intervals of at least one day.
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