451 research outputs found
Mean Field Voter Model of Election to the House of Representatives in Japan
In this study, we propose a mechanical model of a plurality election based on
a mean field voter model. We assume that there are three candidates in each
electoral district, i.e., one from the ruling party, one from the main
opposition party, and one from other political parties. The voters are
classified as fixed supporters and herding (floating) voters with ratios of
and , respectively. Fixed supporters make decisions based on their
information and herding voters make the same choice as another randomly
selected voter. The equilibrium vote-share probability density of herding
voters follows a Dirichlet distribution. We estimate the composition of fixed
supporters in each electoral district and using data from elections to the
House of Representatives in Japan (43rd to 47th). The spatial inhomogeneity of
fixed supporters explains the long-range spatial and temporal correlations. The
estimated values of are close to the estimates obtained from a survey.Comment: 11 pages, 7 figure
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
Data clustering and noise undressing for correlation matrices
We discuss a new approach to data clustering. We find that maximum likelihood
leads naturally to an Hamiltonian of Potts variables which depends on the
correlation matrix and whose low temperature behavior describes the correlation
structure of the data. For random, uncorrelated data sets no correlation
structure emerges. On the other hand for data sets with a built-in cluster
structure, the method is able to detect and recover efficiently that structure.
Finally we apply the method to financial time series, where the low temperature
behavior reveals a non trivial clustering.Comment: 8 pages, 5 figures, completely rewritten and enlarged version of
cond-mat/0003241. Submitted to Phys. Rev.
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
Scaling of the distribution of price fluctuations of individual companies
We present a phenomenological study of stock price fluctuations of individual
companies. We systematically analyze two different databases covering
securities from the three major US stock markets: (a) the New York Stock
Exchange, (b) the American Stock Exchange, and (c) the National Association of
Securities Dealers Automated Quotation stock market. Specifically, we consider
(i) the trades and quotes database, for which we analyze 40 million records for
1000 US companies for the 2-year period 1994--95, and (ii) the Center for
Research and Security Prices database, for which we analyze 35 million daily
records for approximately 16,000 companies in the 35-year period 1962--96. We
study the probability distribution of returns over varying time scales , where varies by a factor of ---from 5 min up to
4 years. For time scales from 5~min up to approximately 16~days, we
find that the tails of the distributions can be well described by a power-law
decay, characterized by an exponent ---well outside the
stable L\'evy regime . For time scales days, we observe results consistent with a slow
convergence to Gaussian behavior. We also analyze the role of cross
correlations between the returns of different companies and relate these
correlations to the distribution of returns for market indices.Comment: 10pages 2 column format with 11 eps figures. LaTeX file requiring
epsf, multicol,revtex. Submitted to PR
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
Noise delayed decay of unstable states: theory versus numerical simulations
We study the noise delayed decay of unstable nonequilibrium states in
nonlinear dynamical systems within the framework of the overdamped Brownian
motion model. We give the exact expressions for the decay times of unstable
states for polynomial potential profiles and obtain nonmonotonic behavior of
the decay times as a function of the noise intensity for the unstable
nonequilibrium states. The analytical results are compared with numerical
simulations.Comment: 9 pages, 6 figures, in press in J. Phys.
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.
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
Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode
We investigate the emergence of a structure in the correlation matrix of
assets' returns as the time-horizon over which returns are computed increases
from the minutes to the daily scale. We analyze data from different stock
markets (New York, Paris, London, Milano) and with different methods. Result
crucially depends on whether the data is restricted to the ``internal''
dynamics of the market, where the ``center of mass'' motion (the market mode)
is removed or not. If the market mode is not removed, we find that the
structure emerges, as the time-horizon increases, from splitting a single large
cluster. In NYSE we find that when the market mode is removed, the structure of
correlation at the daily scale is already well defined at the 5 minutes
time-horizon, and this structure accounts for 80 % of the classification of
stocks in economic sectors. Similar results, though less sharp, are found for
the other markets. We also find that the structure of correlations in the
overnight returns is markedly different from that of intraday activity.Comment: 12 pages, 17 figure
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