Power Laws and Gaussians for Stock Market Fluctuations

The daily volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well long-term trends. We also model the transition to a Gaussian distribution for longer time intervals, like months instead of days.Comment: 7 pages including 4 figure

Modelling financial markets by the multiplicative sequence of trades

We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law probability distribution of the trading activity. The model reproduces the spectral properties of trading activity and explains the mechanism of power-law distribution in real markets.Comment: 6 pages, 2 figure

The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics

The nature of fluctuations in the Indian financial market is analyzed in this paper. We have looked at the price returns of individual stocks, with tick-by-tick data from the National Stock Exchange (NSE) and daily closing price data from both NSE and the Bombay Stock Exchange (BSE), the two largest exchanges in India. We find that the price returns in Indian markets follow a fat-tailed cumulative distribution, consistent with a power law having exponent $\alpha \sim 3$, similar to that observed in developed markets. However, the distributions of trading volume and the number of trades have a different nature than that seen in the New York Stock Exchange (NYSE). Further, the price movement of different stocks are highly correlated in Indian markets.Comment: 10 pages, 7 figures, to appear in Proceedings of International Workshop on "Econophysics of Stock Markets and Minority Games" (Econophys-Kolkata II), Feb 14-17, 200

Price fluctuations from the order book perspective - empirical facts and a simple model

Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit order sizes was found to be consistent with a power law with an exponent close to 2. A somewhat better fit to this distribution was obtained by using a log-normal distribution with an effective power law exponent equal to 2 in the middle of the observed range. The depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non-linear function of its size. A large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a short term deterministic price change, which is in accord with the law of supply and demand.Comment: To appear in proceedings of the NATO Advanced Research Workshop on Application of Physics in Economic Modelling, Prague 2001. 8 figure

Multiplicative point process as a model of trading activity

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f. Furthermore, we analyze the relation between the power-law correlations and the origin of the power-law probability distribution of the signal intensity. We introduce a stochastic multiplicative model for the time intervals between point events and analyze the statistical properties of the signal analytically and numerically. Such model system exhibits power-law spectral density S(f)~1/f**beta for various values of beta, including beta=1/2, 1 and 3/2. Explicit expressions for the power spectra in the low frequency limit and for the distribution density of the interevent time are obtained. The counting statistics of the events is analyzed analytically and numerically, as well. The specific interest of our analysis is related with the financial markets, where long-range correlations of price fluctuations largely depend on the number of transactions. We analyze the spectral density and counting statistics of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power-law distribution of trading activity. The study provides evidence that the statistical properties of the financial markets are enclosed in the statistics of the time interval between trades. A multiplicative point process serves as a consistent model generating this statistics.Comment: 10 pages, 3 figure

Time-reversal asymmetry in Cont-Bouchaud stock market model

The percolation model of stock market speculation allows an asymmetry (in the return distribution) leading to fast downward crashes and slow upward recovery. We see more small upturns and more intermediate downturns.Comment: 2 pages text in TeX, two figures, all in one postscript fil

Dynamical analysis of S&P500 momentum

The dynamics of the S&P500 price signal is studied using a moving average technique. Particular attention is paid to intersections of two moving averages with different time horizons. The distributions of the slopes and angle between two moving averages at intersections is analyzed, as well as that of the waiting times between intersections. In addition, the distribution of maxima and minima in the moving average signal is investigated. In all cases, persistent patterns are observed in these probability measures and it is suggested that such variables be considered for better analysis and possible prediction of the trends of the signal.Comment: 17 pages, 9 figures; to be published in Physica