593 research outputs found
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
Persistence in a Random Bond Ising Model of Socio-Econo Dynamics
We study the persistence phenomenon in a socio-econo dynamics model using
computer simulations at a finite temperature on hypercubic lattices in
dimensions up to 5. The model includes a ` social\rq local field which contains
the magnetization at time . The nearest neighbour quenched interactions are
drawn from a binary distribution which is a function of the bond concentration,
. The decay of the persistence probability in the model depends on both the
spatial dimension and . We find no evidence of ` blocking\rq in this model.
We also discuss the implications of our results for possible applications in
the social and economic fields. It is suggested that the absence, or otherwise,
of blocking could be used as a criterion to decide on the validity of a given
model in different scenarios.Comment: 11 pages, 4 figure
Sector identification in a set of stock return time series traded at the London Stock Exchange
We compare some methods recently used in the literature to detect the
existence of a certain degree of common behavior of stock returns belonging to
the same economic sector. Specifically, we discuss methods based on random
matrix theory and hierarchical clustering techniques. We apply these methods to
a portfolio of stocks traded at the London Stock Exchange. The investigated
time series are recorded both at a daily time horizon and at a 5-minute time
horizon. The correlation coefficient matrix is very different at different time
horizons confirming that more structured correlation coefficient matrices are
observed for long time horizons. All the considered methods are able to detect
economic information and the presence of clusters characterized by the economic
sector of stocks. However different methods present a different degree of
sensitivity with respect to different sectors. Our comparative analysis
suggests that the application of just a single method could not be able to
extract all the economic information present in the correlation coefficient
matrix of a stock portfolio.Comment: 28 pages, 13 figures, 3 Tables. Proceedings of the conference on
"Applications of Random Matrices to Economy and other Complex Systems",
Krakow (Poland), May 25-28 2005. Submitted for pubblication to Acta Phys. Po
Wealth redistribution with finite resources
We present a simplified model for the exploitation of finite resources by
interacting agents, where each agent receives a random fraction of the
available resources. An extremal dynamics ensures that the poorest agent has a
chance to change its economic welfare. After a long transient, the system
self-organizes into a critical state that maximizes the average performance of
each participant. Our model exhibits a new kind of wealth condensation, where
very few extremely rich agents are stable in time and the rest stays in the
middle class.Comment: 4 pages, 3 figures, RevTeX 4 styl
Hollywood blockbusters and long-tailed distributions: An empirical study of the popularity of movies
Numerical data for all movies released in theaters in the USA during the
period 1997-2003 are examined for the distribution of their popularity in terms
of (i) the number of weeks they spent in the Top 60 according to the weekend
earnings, and (ii) the box-office gross during the opening week, as well as,
the total duration for which they were shown in theaters. These distributions
show long tails where the most popular movies are located. Like the study of
Redner [S. Redner, Eur. Phys. J. B 4, 131 (1998)] on the distribution of
citations to individual papers, our results are consistent with a power-law
dependence of the rank distribution of gross revenues for the most popular
movies with a exponent close to -1/2.Comment: 4 pages, 4 figure
Networks of equities in financial markets
We review the recent approach of correlation based networks of financial
equities. We investigate portfolio of stocks at different time horizons,
financial indices and volatility time series and we show that meaningful
economic information can be extracted from noise dressed correlation matrices.
We show that the method can be used to falsify widespread market models by
directly comparing the topological properties of networks of real and
artificial markets.Comment: 9 pages, 8 figures. Accepted for publication in EPJ
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.
Quantifying dynamics of the financial correlations
A novel application of the correlation matrix formalism to study dynamics of
the financial evolution is presented. This formalism allows to quantify the
memory effects as well as some potential repeatable intradaily structures in
the financial time-series. The present study is based on the high-frequency
Deutsche Aktienindex (DAX) data over the time-period between November 1997 and
December 1999 and demonstrates a power of the method. In this way two
significant new aspects of the DAX evolution are identified: (i) the memory
effects turn out to be sizably shorter than what the standard autocorrelation
function analysis seems to indicate and (ii) there exist short term repeatable
structures in fluctuations that are governed by a distinct dynamics. The former
of these results may provide an argument in favour of the market efficiency
while the later one may indicate origin of the difficulty in reaching a
Gaussian limit, expected from the central limit theorem, in the distribution of
returns on longer time-horizons.Comment: 10 pages, 7 PostScript figures, talk presented by the first Author at
the NATO ARW on Econophysics, Prague, February 8-10, 2001; to be published in
proceedings (Physica A
Evaluation of Tranche in Securitization and Long-range Ising Model
This econophysics work studies the long-range Ising model of a finite system
with spins and the exchange interaction and the external
field as a modely for homogeneous credit portfolio of assets with default
probability and default correlation . Based on the discussion
on the phase diagram, we develop a perturbative calculation method for
the model and obtain explicit expressions for and the
normalization factor in terms of the model parameters and . The
effect of the default correlation on the probabilities
for defaults and on the cumulative distribution
function are discussed. The latter means the average loss rate
of the``tranche'' (layered structure) of the securities (e.g. CDO), which are
synthesized from a pool of many assets. We show that the expected loss rate of
the subordinated tranche decreases with and that of the senior
tranche increases linearly, which are important in their pricing and ratings.Comment: 21 pages, 9 figure
- …