521 research outputs found
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
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
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
, 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
Simple model of a limit order-driven market
We introduce and study a simple model of a limit order-driven market. Traders
in this model can either trade at the market price or place a limit order, i.e.
an instruction to buy (sell) a certain amount of the stock if its price falls
below (raises above) a predefined level. The choice between these two options
is purely random (there are no strategies involved), and the execution price of
a limit order is determined simply by offsetting the most recent market price
by a random amount. Numerical simulations of this model revealed that despite
such minimalistic rules the price pattern generated by the model has such
realistic features as ``fat'' tails of the price fluctuations distribution,
characterized by a crossover between two power law exponents, long range
correlations of the volatility, and a non-trivial Hurst exponent of the price
signal.Comment: 4 pages, 3 fugure
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
Modeling of waiting times and price changes in currency exchange data
A theory which describes the share price evolution at financial markets as a
continuous-time random walk has been generalized in order to take into account
the dependence of waiting times t on price returns x. A joint probability
density function (pdf) which uses the concept of a L\'{e}vy stable distribution
is worked out. The theory is fitted to high-frequency US$/Japanese Yen exchange
rate and low-frequency 19th century Irish stock data. The theory has been
fitted both to price return and to waiting time data and the adherence to data,
in terms of the chi-squared test statistic, has been improved when compared to
the old theory.Comment: 22 pages, 5 postscript figures, LaTeX2e using elsart.cl
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
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