129 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
Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions
The clustering of companies within a specific stock market index is studied
by means of super-paramagnetic transitions of an appropriate q-state Potts
model where the spins correspond to companies and the interactions are
functions of the correlation coefficients determined from the time dependence
of the companies' individual stock prices. The method is a generalization of
the clustering algorithm by Domany et. al. to the case of anti-ferromagnetic
interactions corresponding to anti-correlations. For the Dow Jones Industrial
Average where no anti-correlations were observed in the investigated time
period, the previous results obtained by different tools were well reproduced.
For the Standard & Poor's 500, where anti-correlations occur, repulsion between
stocks modify the cluster structure.Comment: 4 pages; changed conten
An interest rates cluster analysis
An empirical analysis of interest rates in money and capital markets is
performed. We investigate a set of 34 different weekly interest rate time
series during a time period of 16 years between 1982 and 1997. Our study is
focused on the collective behavior of the stochastic fluctuations of these
time-series which is investigated by using a clustering linkage procedure.
Without any a priori assumption, we individuate a meaningful separation in 6
main clusters organized in a hierarchical structure.Comment: 7 pages, 7 figure
An Outlook on Correlations in Stock Prices
We present an outlook of the studies on correlations in the price timeseries
of stocks, discussing the construction and applications of "asset tree". The
topic discussed here should illustrate how the complex economic system
(financial market) enrichens the list of existing dynamical systems that
physicists have been studying for long.Comment: 6 pages, RevTeX format. To appear in the Conference Proceedings of
ECONOPHYS-KOLKATA II: International Workshop on Econophysics of Stock Markets
and Minority Games", February 14-17, 2006, SINP, Kolkata, as a book chapter
in Eds. A. Chatterjee and B.K. Chakrabarti, Econophysics of Stock and other
Markets, (Springer-Verlag (Italia), Milan, 2006
Variety and Volatility in Financial Markets
We study the price dynamics of stocks traded in a financial market by
considering the statistical properties both of a single time series and of an
ensemble of stocks traded simultaneously. We use the stocks traded in the
New York Stock Exchange to form a statistical ensemble of daily stock returns.
For each trading day of our database, we study the ensemble return
distribution. We find that a typical ensemble return distribution exists in
most of the trading days with the exception of crash and rally days and of the
days subsequent to these extreme events. We analyze each ensemble return
distribution by extracting its first two central moments. We observe that these
moments are fluctuating in time and are stochastic processes themselves. We
characterize the statistical properties of ensemble return distribution central
moments by investigating their probability density functions and temporal
correlation properties. In general, time-averaged and portfolio-averaged price
returns have different statistical properties. We infer from these differences
information about the relative strength of correlation between stocks and
between different trading days. Lastly, we compare our empirical results with
those predicted by the single-index model and we conclude that this simple
model is unable to explain the statistical properties of the second moment of
the ensemble return distribution.Comment: 10 pages, 11 figure
Kolkata Restaurant Problem as a generalised El Farol Bar Problem
Generalisation of the El Farol bar problem to that of many bars here leads to
the Kolkata restaurant problem, where the decision to go to any restaurant or
not is much simpler (depending on the previous experience of course, as in the
El Farol bar problem). This generalised problem can be exactly analysed in some
limiting cases discussed here. The fluctuation in the restaurant service can be
shown to have precisely an inverse cubic behavior, as widely seen in the stock
market fluctuations.Comment: 2 column RevTeX4, 4 pages, 3 eps figs; to be published in
'Econophysics of Markets and Business Networks', [Proc. Econophys-Kolkata
III], Eds. A. Chatterjee, B. K. Chakrabarti, New Economic Windows Series,
Springer, Milan, 2007, pp. 220-22
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.
An Efficient Adaptive Distributed Space-Time Coding Scheme for Cooperative Relaying
A non-regenerative dual-hop wireless system based on a distributed space-time
coding strategy is considered. It is assumed that each relay retransmits an
appropriately scaled space-time coded version of its received signal. The main
goal of this paper is to investigate a power allocation strategy in relay
stations, which is based on minimizing the outage probability. In the high
signal-to-noise ratio regime for the relay-destination link, it is shown that a
threshold-based power allocation scheme (i.e., the relay remains silent if its
channel gain with the source is less than a prespecified threshold) is optimum.
Monte-Carlo simulations show that the derived on-off power allocation scheme
performs close to optimum for finite signal-to-noise ratio values. Numerical
results demonstrate a dramatic improvement in system performance as compared to
the case that the relay stations forward their received signals with full
power. In addition, a hybrid amplify-and-forward/detect-and-forward scheme is
proposed for the case that the quality of the source-relay link is good.
Finally, the robustness of the proposed scheme in the presence of channel
estimation errors is numerically evaluated.Comment: submitted to IEEE Transactions on Wireless Communications (24 pages
Brazilian elections: voting for a scaling democracy
The proportional elections held in Brazil in 1998 and 2002 display identical
statistical signatures. In particular, the distribution of votes among
candidates includes a power-law regimen. We suggest that the rationale behind
this robust scaling invariance is a multiplicative process in which the voter's
choice for a candidate is governed by a product of probabilities.Comment: 4 pages, 2 figure
The dynamics of financial stability in complex networks
We address the problem of banking system resilience by applying
off-equilibrium statistical physics to a system of particles, representing the
economic agents, modelled according to the theoretical foundation of the
current banking regulation, the so called Merton-Vasicek model. Economic agents
are attracted to each other to exchange `economic energy', forming a network of
trades. When the capital level of one economic agent drops below a minimum, the
economic agent becomes insolvent. The insolvency of one single economic agent
affects the economic energy of all its neighbours which thus become susceptible
to insolvency, being able to trigger a chain of insolvencies (avalanche). We
show that the distribution of avalanche sizes follows a power-law whose
exponent depends on the minimum capital level. Furthermore, we present evidence
that under an increase in the minimum capital level, large crashes will be
avoided only if one assumes that agents will accept a drop in business levels,
while keeping their trading attitudes and policies unchanged. The alternative
assumption, that agents will try to restore their business levels, may lead to
the unexpected consequence that large crises occur with higher probability
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