219 research outputs found
Rational Decisions, Random Matrices and Spin Glasses
We consider the problem of rational decision making in the presence of
nonlinear constraints. By using tools borrowed from spin glass and random
matrix theory, we focus on the portfolio optimisation problem. We show that the
number of ``optimal'' solutions is generically exponentially large: rationality
is thus de facto of limited use. In addition, this problem is related to spin
glasses with L\'evy-like (long-ranged) couplings, for which we show that the
ground state is not exponentially degenerate
Correlation structure of extreme stock returns
It is commonly believed that the correlations between stock returns increase
in high volatility periods. We investigate how much of these correlations can
be explained within a simple non-Gaussian one-factor description with time
independent correlations. Using surrogate data with the true market return as
the dominant factor, we show that most of these correlations, measured by a
variety of different indicators, can be accounted for. In particular, this
one-factor model can explain the level and asymmetry of empirical exceedance
correlations. However, more subtle effects require an extension of the one
factor model, where the variance and skewness of the residuals also depend on
the market return.Comment: Substantial rewriting. Added exceedance correlations, removed some
confusing material. To appear in Quantitative Financ
Ensemble properties of securities traded in the NASDAQ market
We study the price dynamics of stocks traded in the NASDAQ market by
considering the statistical properties of an ensemble of stocks traded
simultaneously. For each trading day of our database, we study the ensemble
return distribution by extracting its first two central moments. According to
previous results obtained for the NYSE market, we find that the second moment
is a long-range correlated variable. We compare time-averaged and
ensemble-averaged price returns and we show that the two averaging procedures
lead to different statistical results.Comment: 7 pages, 3 figures, to appear in the proceedings of NATO ARW on
Application of Physics in Economic Modelling, Prague, 8-10 February 200
How Three Millennials Revolutionized a Global Industry
This study will examine the ways in which Airbnb has disrupted both the hospitality and travel industries. Through an analysis of their business expansions into new markets and business lines, this study will reveal the importance of their acquisitions and technological innovations for future growth. The founders of Airbnb have continued to challenge the status quo in order to build a revolutionary business that will forever transform the global travel industry
From turbulence to financial time series
We develop a framework especially suited to the autocorrelation properties
observed in financial times series, by borrowing from the physical picture of
turbulence. The success of our approach as applied to high frequency foreign
exchange data is demonstrated by the overlap of the curves in Figure (1), since
we are able to provide an analytical derivation of the relative sizes of the
quantities depicted. These quantities include departures from Gaussian
probability density functions and various two and three-point autocorrelation
functions.Comment: 10 pages, 1 figure, LaTeX, version to appear in Physica
Volatility in the Italian Stock Market: an Empirical Study
We study the volatility of the MIB30-stock-index high-frequency data from
November 28, 1994 through September 15, 1995. Our aim is to empirically
characterize the volatility random walk in the framework of continuous-time
finance. To this end, we compute the index volatility by means of the
log-return standard deviation. We choose an hourly time window in order to
investigate intraday properties of volatility. A periodic component is found
for the hourly time window, in agreement with previous observations.
Fluctuations are studied by means of detrended fluctuation analysis, and we
detect long-range correlations. Volatility values are log-stable distributed.
We discuss the implications of these results for stochastic volatility
modelling.Comment: 9 pages, 4 figures, LaTeX2e, to be published in Physica
Volatility in Financial Markets: Stochastic Models and Empirical Results
We investigate the historical volatility of the 100 most capitalized stocks
traded in US equity markets. An empirical probability density function (pdf) of
volatility is obtained and compared with the theoretical predictions of a
lognormal model and of the Hull and White model. The lognormal model well
describes the pdf in the region of low values of volatility whereas the Hull
and White model better approximates the empirical pdf for large values of
volatility. Both models fails in describing the empirical pdf over a moderately
large volatility range.Comment: 6 pages, 2 figure
Stability of the replica-symmetric saddle-point in general mean-field spin-glass models
Within the replica approach to mean-field spin-glasses the transition from
ergodic high-temperature behaviour to the glassy low-temperature phase is
marked by the instability of the replica-symmetric saddle-point. For general
spin-glass models with non-Gaussian field distributions the corresponding
Hessian is a matrix with the number of replicas tending to
zero eventually. We block-diagonalize this Hessian matrix using representation
theory of the permutation group and identify the blocks related to the
spin-glass susceptibility. Performing the limit within these blocks we
derive expressions for the de~Almeida-Thouless line of general spin-glass
models. Specifying these expressions to the cases of the
Sherrington-Kirkpatrick, Viana-Bray, and the L\'evy spin glass respectively we
obtain results in agreement with previous findings using the cavity approach
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