549 research outputs found
Correlation, hierarchies, and networks in financial markets
We discuss some methods to quantitatively investigate the properties of
correlation matrices. Correlation matrices play an important role in portfolio
optimization and in several other quantitative descriptions of asset price
dynamics in financial markets. Specifically, we discuss how to define and
obtain hierarchical trees, correlation based trees and networks from a
correlation matrix. The hierarchical clustering and other procedures performed
on the correlation matrix to detect statistically reliable aspects of the
correlation matrix are seen as filtering procedures of the correlation matrix.
We also discuss a method to associate a hierarchically nested factor model to a
hierarchical tree obtained from a correlation matrix. The information retained
in filtering procedures and its stability with respect to statistical
fluctuations is quantified by using the Kullback-Leibler distance.Comment: 37 pages, 9 figures, 3 table
Dynamics of fintech terms in news and blogs and specialization of companies of the fintech industry
We perform a large scale analysis of a list of fintech terms in (i) news and blogs in the English language and (ii) professional descriptions of companies operating in many countries. The occurrence and the co-occurrence of fintech terms and locutions show a progressive evolution of the list of fintech terms in a compact and coherent set of terms used worldwide to describe fintech business activities. By using methods of complex networks that are specifically designed to deal with heterogeneous systems, our analysis of a large set of professional descriptions of companies shows that companies having fintech terms in their description present over-expressions of specific attributes of country, municipality, and economic sector. By using the approach of statistically validated networks, we detect geographical and economic over-expressions of a set of companies related to the multi-industry, geographically, and economically distributed fintech movement
Economic sector identification in a set of stocks traded at the New York Stock Exchange: a comparative analysis
We review 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 set of stocks traded at the New York Stock Exchange. The investigated time
series are recorded at a daily time horizon.
All the considered methods are able to detect economic information and the
presence of clusters characterized by the economic sector of stocks. However,
different methodologies provide different information about the considered set.
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 set of stocks.Comment: 13 pages, 8 figures, 2 Table
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
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
Stock markets and quantum dynamics: a second quantized description
In this paper we continue our descriptions of stock markets in terms of some
non abelian operators which are used to describe the portfolio of the various
traders and other {\em observable} quantities. After a first prototype model
with only two traders, we discuss a more realistic model of market with an
arbitrary number of traders. For both models we find approximated solutions for
the time evolution of the portfolio of each trader. In particular, for the more
realistic model, we use the {\em stochastic limit} approach and a {\em fixed
point like} approximation
Detecting informative higher-order interactions in statistically validated hypergraphs
Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the extensive literature on networks, detecting informative hyperlinks in real world hypergraphs is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply our method to a class of synthetic benchmarks and to several datasets, showing that the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way, to the best of our knowledge, to obtain statistically validated hypergraphs, separating informative connections from noisy ones
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
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
Simplified stock markets described by number operators
In this paper we continue our systematic analysis of the operatorial approach
previously proposed in an economical context and we discuss a {\em mixed} toy
model of a simplified stock market, i.e. a model in which the price of the
shares is given as an input. We deduce the time evolution of the portfolio of
the various traders of the market, as well as of other {\em observable}
quantities. As in a previous paper, we solve the equations of motion by means
of a {\em fixed point like} approximation.Comment: Rep. on Math. Phys., in pres
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