203 research outputs found
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
A model for correlations in stock markets
We propose a group model for correlations in stock markets. In the group
model the markets are composed of several groups, within which the stock price
fluctuations are correlated. The spectral properties of empirical correlation
matrices reported in [Phys. Rev. Lett. {\bf 83}, 1467 (1999); Phys. Rev. Lett.
{\bf 83}, 1471 (1999.)] are well understood from the model. It provides the
connection between the spectral properties of the empirical correlation matrix
and the structure of correlations in stock markets.Comment: two pages including one EPS file for a figur
Portfolio Optimization and the Random Magnet Problem
Diversification of an investment into independently fluctuating assets
reduces its risk. In reality, movement of assets are are mutually correlated
and therefore knowledge of cross--correlations among asset price movements are
of great importance. Our results support the possibility that the problem of
finding an investment in stocks which exposes invested funds to a minimum level
of risk is analogous to the problem of finding the magnetization of a random
magnet. The interactions for this ``random magnet problem'' are given by the
cross-correlation matrix {\bf \sf C} of stock returns. We find that random
matrix theory allows us to make an estimate for {\bf \sf C} which outperforms
the standard estimate in terms of constructing an investment which carries a
minimum level of risk.Comment: 12 pages, 4 figures, revte
The Apparent Madness of Crowds: Irrational collective behavior emerging from interactions among rational agents
Standard economic theory assumes that agents in markets behave rationally.
However, the observation of extremely large fluctuations in the price of
financial assets that are not correlated to changes in their fundamental value,
as well as the extreme instance of financial bubbles and crashes, imply that
markets (at least occasionally) do display irrational behavior. In this paper,
we briefly outline our recent work demonstrating that a market with interacting
agents having bounded rationality can display price fluctuations that are {\em
quantitatively} similar to those seen in real markets.Comment: 4 pages, 1 figure, to appear in Proceedings of International Workshop
on "Econophysics of Stock Markets and Minority Games" (Econophys-Kolkata II),
Feb 14-17, 200
Quantifying Stock Price Response to Demand Fluctuations
We address the question of how stock prices respond to changes in demand. We
quantify the relations between price change over a time interval
and two different measures of demand fluctuations: (a) , defined as the
difference between the number of buyer-initiated and seller-initiated trades,
and (b) , defined as the difference in number of shares traded in buyer
and seller initiated trades. We find that the conditional expectations and of price change for a given or
are both concave. We find that large price fluctuations occur when demand is
very small --- a fact which is reminiscent of large fluctuations that occur at
critical points in spin systems, where the divergent nature of the response
function leads to large fluctuations.Comment: 4 pages (multicol fomat, revtex
The Grounds For Time Dependent Market Potentials From Dealers' Dynamics
We apply the potential force estimation method to artificial time series of
market price produced by a deterministic dealer model. We find that dealers'
feedback of linear prediction of market price based on the latest mean price
changes plays the central role in the market's potential force. When markets
are dominated by dealers with positive feedback the resulting potential force
is repulsive, while the effect of negative feedback enhances the attractive
potential force.Comment: 9 pages, 3 figures, proceedings of APFA
Why do Hurst exponents of traded value increase as the logarithm of company size?
The common assumption of universal behavior in stock market data can
sometimes lead to false conclusions. In statistical physics, the Hurst
exponents characterizing long-range correlations are often closely related to
universal exponents. We show, that in the case of time series of the traded
value, these Hurst exponents increase logarithmically with company size, and
thus are non-universal. Moreover, the average transaction size shows scaling
with the mean transaction frequency for large enough companies. We present a
phenomenological scaling framework that properly accounts for such
dependencies.Comment: 10 pages, 4 figures, to appear in the Proceedings of the
International Workshop on Econophysics of Stock Markets and Minority Games,
Calcutta, 200
Long-Time Fluctuations in a Dynamical Model of Stock Market Indices
Financial time series typically exhibit strong fluctuations that cannot be
described by a Gaussian distribution. In recent empirical studies of stock
market indices it was examined whether the distribution P(r) of returns r(tau)
after some time tau can be described by a (truncated) Levy-stable distribution
L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot
be expressed in a closed form, one can identify its parameters by testing the
dependence of the central peak height on tau as well as the power-law decay of
the tails. In an earlier study [Mantegna and Stanley, Nature 376, 46 (1995)] it
was found that the behavior of the central peak of P(r) for the Standard & Poor
500 index is consistent with the Levy distribution with alpha=1.4. In a more
recent study [Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found
that the tails of P(r) exhibit a power-law decay with an exponent alpha ~= 3,
thus deviating from the Levy distribution. In this paper we study the
distribution of returns in a generic model that describes the dynamics of stock
market indices. For the distributions P(r) generated by this model, we observe
that the scaling of the central peak is consistent with a Levy distribution
while the tails exhibit a power-law distribution with an exponent alpha > 2,
namely beyond the range of Levy-stable distributions. Our results are in
agreement with both empirical studies and reconcile the apparent disagreement
between their results
Analysis of aggregated tick returns: evidence for anomalous diffusion
In order to investigate the origin of large price fluctuations, we analyze
stock price changes of ten frequently traded NASDAQ stocks in the year 2002.
Though the influence of the trading frequency on the aggregate return in a
certain time interval is important, it cannot alone explain the heavy tailed
distribution of stock price changes. For this reason, we analyze intervals with
a fixed number of trades in order to eliminate the influence of the trading
frequency and investigate the relevance of other factors for the aggregate
return. We show that in tick time the price follows a discrete diffusion
process with a variable step width while the difference between the number of
steps in positive and negative direction in an interval is Gaussian
distributed. The step width is given by the return due to a single trade and is
long-term correlated in tick time. Hence, its mean value can well characterize
an interval of many trades and turns out to be an important determinant for
large aggregate returns. We also present a statistical model reproducing the
cumulative distribution of aggregate returns. For an accurate agreement with
the empirical distribution, we also take into account asymmetries of the step
widths in different directions together with crosscorrelations between these
asymmetries and the mean step width as well as the signs of the steps.Comment: 9 pages, 10 figures, typos correcte
Stock mechanics: predicting recession in S&P500, DJIA, and NASDAQ
An original method, assuming potential and kinetic energy for prices and
conservation of their sum is developed for forecasting exchanges. Connections
with power law are shown. Semiempirical applications on S&P500, DJIA, and
NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock
Exchange index ISE-100 is found involving a potential to continue to rise.Comment: 14 pages, 4 figure
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