246 research outputs found
Collective behavior of stock price movements in an emerging market
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 of distinct sector
identity in emerging markets is explicitly shown by reconstructing the network
of mutually interacting stocks. Spectral analysis of C for NSE reveals that,
the few largest eigenvalues deviate from the bulk of the spectrum predicted by
random matrix theory, but they are far fewer in number compared to, e.g., NYSE.
We show this to be due to the relative weakness of intra-sector interactions
between stocks, compared to the market mode, by modeling stock price dynamics
with a two-factor model. Our results suggest that the emergence of an internal
structure comprising multiple groups of strongly coupled components is a
signature of market development.Comment: 10 pages, 10 figure
Stochastic Opinion Formation in Scale-Free Networks
The dynamics of opinion formation in large groups of people is a complex
non-linear phenomenon whose investigation is just at the beginning. Both
collective behaviour and personal view play an important role in this
mechanism. In the present work we mimic the dynamics of opinion formation of a
group of agents, represented by two state , as a stochastic response of
each of them to the opinion of his/her neighbours in the social network and to
feedback from the average opinion of the whole. In the light of recent studies,
a scale-free Barab\'asi-Albert network has been selected to simulate the
topology of the interactions. A turbulent-like dynamics, characterized by an
intermittent behaviour, is observed for a certain range of the model
parameters. The problem of uncertainty in decision taking is also addressed
both from a topological point of view, using random and targeted removal of
agents from the network, and by implementing a three state model, where the
third state, zero, is related to the information available to each agent.
Finally, the results of the model are tested against the best known network of
social interactions: the stock market. A time series of daily closures of the
Dow Jones index has been used as an indicator of the possible applicability of
our model in the financial context. Good qualitative agreement is found.Comment: 24 pages and 13 figures, Physical Review E, in pres
Amnestically induced persistence in random walks
We study how the Hurst exponent depends on the fraction of the
total time remembered by non-Markovian random walkers that recall only the
distant past. We find that otherwise nonpersistent random walkers switch to
persistent behavior when inflicted with significant memory loss. Such memory
losses induce the probability density function of the walker's position to
undergo a transition from Gaussian to non-Gaussian. We interpret these findings
of persistence in terms of a breakdown of self-regulation mechanisms and
discuss their possible relevance to some of the burdensome behavioral and
psychological symptoms of Alzheimer's disease and other dementias.Comment: 4 pages, 3 figs, subm. to Phys. Rev. Let
Mean Escape Time in a System with Stochastic Volatility
We study the mean escape time in a market model with stochastic volatility.
The process followed by the volatility is the Cox Ingersoll and Ross process
which is widely used to model stock price fluctuations. The market model can be
considered as a generalization of the Heston model, where the geometric
Brownian motion is replaced by a random walk in the presence of a cubic
nonlinearity. We investigate the statistical properties of the escape time of
the returns, from a given interval, as a function of the three parameters of
the model. We find that the noise can have a stabilizing effect on the system,
as long as the global noise is not too high with respect to the effective
potential barrier experienced by a fictitious Brownian particle. We compare the
probability density function of the return escape times of the model with those
obtained from real market data. We find that they fit very well.Comment: 9 pages, 9 figures, to be published in Phys. Rev.
Recurrence of biased quantum walks on a line
The Polya number of a classical random walk on a regular lattice is known to
depend solely on the dimension of the lattice. For one and two dimensions it
equals one, meaning unit probability to return to the origin. This result is
extremely sensitive to the directional symmetry, any deviation from the equal
probability to travel in each direction results in a change of the character of
the walk from recurrent to transient. Applying our definition of the Polya
number to quantum walks on a line we show that the recurrence character of
quantum walks is more stable against bias. We determine the range of parameters
for which biased quantum walks remain recurrent. We find that there exist
genuine biased quantum walks which are recurrent.Comment: Journal reference added, minor corrections in the tex
Fluctuations of company yearly profits versus scaled revenue: Fat tail distribution of Levy type
We analyze annual revenues and earnings data for the 500 largest-revenue U.S.
companies during the period 1954-2007. We find that mean year profits are
proportional to mean year revenues, exception made for few anomalous years,
from which we postulate a linear relation between company expected mean profit
and revenue. Mean annual revenues are used to scale both company profits and
revenues. Annual profit fluctuations are obtained as difference between actual
annual profit and its expected mean value, scaled by a power of the revenue to
get a stationary behavior as a function of revenue. We find that profit
fluctuations are broadly distributed having approximate power-law tails with a
Levy-type exponent , from which we derive the associated
break-even probability distribution. The predictions are compared with
empirical data.Comment: 6 pages, 6 figure
Stochastic Cellular Automata Model for Stock Market Dynamics
In the present work we introduce a stochastic cellular automata model in
order to simulate the dynamics of the stock market. A direct percolation method
is used to create a hierarchy of clusters of active traders on a two
dimensional grid. Active traders are characterised by the decision to buy,
(+1), or sell, (-1), a stock at a certain discrete time step. The remaining
cells are inactive,(0). The trading dynamics is then determined by the
stochastic interaction between traders belonging to the same cluster. Most of
the stylized aspects of the financial market time series are reproduced by the
model.Comment: 17 pages and 7 figure
Scaling of the distribution of fluctuations of financial market indices
We study the distribution of fluctuations over a time scale (i.e.,
the returns) of the S&P 500 index by analyzing three distinct databases.
Database (i) contains approximately 1 million records sampled at 1 min
intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily
records for the 35-year period 1962-1996, and database (iii) contains 852
monthly records for the 71-year period 1926-1996. We compute the probability
distributions of returns over a time scale , where varies
approximately over a factor of 10^4 - from 1 min up to more than 1 month. We
find that the distributions for 4 days (1560 mins) are
consistent with a power-law asymptotic behavior, characterized by an exponent
, well outside the stable L\'evy regime . To
test the robustness of the S&P result, we perform a parallel analysis on two
other financial market indices. Database (iv) contains 3560 daily records of
the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649
daily records of the Hang-Seng index for the 18-year period 1980-97. We find
estimates of consistent with those describing the distribution of S&P
500 daily-returns. One possible reason for the scaling of these distributions
is the long persistence of the autocorrelation function of the volatility. For
time scales longer than days, our results are
consistent with slow convergence to Gaussian behavior.Comment: 12 pages in multicol LaTeX format with 27 postscript figures
(Submitted to PRE May 20, 1999). See
http://polymer.bu.edu/~amaral/Professional.html for more of our work on this
are
Brownian Motions on Metric Graphs
Brownian motions on a metric graph are defined. Their generators are
characterized as Laplace operators subject to Wentzell boundary at every
vertex. Conversely, given a set of Wentzell boundary conditions at the vertices
of a metric graph, a Brownian motion is constructed pathwise on this graph so
that its generator satisfies the given boundary conditions.Comment: 43 pages, 7 figures. 2nd revision of our article 1102.4937: The
introduction has been modified, several references were added. This article
will appear in the special issue of Journal of Mathematical Physics
celebrating Elliott Lieb's 80th birthda
Quasi-Elastic Scattering in the Inclusive (He, t) Reaction
The triton energy spectra of the charge-exchange C(He,t) reaction
at 2 GeV beam energy are analyzed in the quasi-elastic nucleon knock-out
region. Considering that this region is mainly populated by the charge-exchange
of a proton in He with a neutron in the target nucleus and the final proton
going in the continuum, the cross-sections are written in the distorted-wave
impulse approximation. The t-matrix for the elementary exchange process is
constructed in the DWBA, using one pion- plus rho-exchange potential for the
spin-isospin nucleon- nucleon potential. This t-matrix reproduces the
experimental data on the elementary pn np process. The calculated
cross-sections for the C(He,t) reaction at to triton
emission angle are compared with the corresponding experimental data, and are
found in reasonable overall accord.Comment: 19 pages, latex, 11 postscript figures available at
[email protected], submitted to Phy.Rev.
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