450 research outputs found
Memory-induced anomalous dynamics: emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model
We present a random walk model that exhibits asymptotic subdiffusive,
diffusive, and superdiffusive behavior in different parameter regimes. This
appears to be the first instance of a single random walk model leading to all
three forms of behavior by simply changing parameter values. Furthermore, the
model offers the great advantage of analytic tractability. Our model is
non-Markovian in that the next jump of the walker is (probabilistically)
determined by the history of past jumps. It also has elements of intermittency
in that one possibility at each step is that the walker does not move at all.
This rich encompassing scenario arising from a single model provides useful
insights into the source of different types of asymptotic behavior
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
Evolution and anti-evolution in a minimal stock market model
We present a novel microscopic stock market model consisting of a large
number of random agents modeling traders in a market. Each agent is
characterized by a set of parameters that serve to make iterated predictions of
two successive returns. The future price is determined according to the offer
and the demand of all agents. The system evolves by redistributing the capital
among the agents in each trading cycle. Without noise the dynamics of this
system is nearly regular and thereby fails to reproduce the stochastic return
fluctuations observed in real markets. However, when in each cycle a small
amount of noise is introduced we find the typical features of real financial
time series like fat-tails of the return distribution and large temporal
correlations in the volatility without significant correlations in the price
returns. Introducing the noise by an evolutionary process leads to different
scalings of the return distributions that depend on the definition of fitness.
Because our realistic model has only very few parameters, and the results
appear to be robust with respect to the noise level and the number of agents we
expect that our framework may serve as new paradigm for modeling self generated
return fluctuations in markets.Comment: 13 pages, 5 figure
Determinants of immediate price impacts at the trade level in an emerging order-driven market
The common wisdom argues that, in general, large trades cause large price
changes, while small trades cause small price changes. However, for extremely
large price changes, the trade size and news play a minor role, while the
liquidity (especially price gaps on the limit order book) is a more influencing
factor. Hence, there might be other influencing factors of immediate price
impacts of trades. In this paper, through mechanical analysis of price
variations before and after a trade of arbitrary size, we identify that the
trade size, the bid-ask spread, the price gaps and the outstanding volumes at
the bid and ask sides of the limit order book have impacts on the changes of
prices. We propose two regression models to investigate the influences of these
microscopic factors on the price impact of buyer-initiated partially filled
trades, seller-initiated partially filled trades, buyer-initiated filled
trades, and seller-initiated filled trades. We find that they have
quantitatively similar explanation powers and these factors can account for up
to 44% of the price impacts. Large trade sizes, wide bid-ask spreads, high
liquidity at the same side and low liquidity at the opposite side will cause a
large price impact. We also find that the liquidity at the opposite side has a
more influencing impact than the liquidity at the same side. Our results shed
new lights on the determinants of immediate price impacts.Comment: 21 IOP tex pages including 5 figures and 5 tables. Accepted for
publication in New Journal of Physic
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
Record statistics for biased random walks, with an application to financial data
We consider the occurrence of record-breaking events in random walks with
asymmetric jump distributions. The statistics of records in symmetric random
walks was previously analyzed by Majumdar and Ziff and is well understood.
Unlike the case of symmetric jump distributions, in the asymmetric case the
statistics of records depends on the choice of the jump distribution. We
compute the record rate , defined as the probability for the th
value to be larger than all previous values, for a Gaussian jump distribution
with standard deviation that is shifted by a constant drift . For
small drift, in the sense of , the correction to
grows proportional to arctan and saturates at the value
. For large the record rate approaches a
constant, which is approximately given by
for .
These asymptotic results carry over to other continuous jump distributions with
finite variance. As an application, we compare our analytical results to the
record statistics of 366 daily stock prices from the Standard & Poors 500
index. The biased random walk accounts quantitatively for the increase in the
number of upper records due to the overall trend in the stock prices, and after
detrending the number of upper records is in good agreement with the symmetric
random walk. However the number of lower records in the detrended data is
significantly reduced by a mechanism that remains to be identified.Comment: 16 pages, 7 figure
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.
Spurious trend switching phenomena in financial markets
The observation of power laws in the time to extrema of volatility, volume
and intertrade times, from milliseconds to years, are shown to result
straightforwardly from the selection of biased statistical subsets of
realizations in otherwise featureless processes such as random walks. The bias
stems from the selection of price peaks that imposes a condition on the
statistics of price change and of trade volumes that skew their distributions.
For the intertrade times, the extrema and power laws results from the format of
transaction data
Fluctuations of company yearly profits versus scaled revenue: Fat tail distribution of Levy type
We analyze annual revenues and earnings data for the 500 largest-revenue U.S.
companies during the period 1954-2007. We find that mean year profits are
proportional to mean year revenues, exception made for few anomalous years,
from which we postulate a linear relation between company expected mean profit
and revenue. Mean annual revenues are used to scale both company profits and
revenues. Annual profit fluctuations are obtained as difference between actual
annual profit and its expected mean value, scaled by a power of the revenue to
get a stationary behavior as a function of revenue. We find that profit
fluctuations are broadly distributed having approximate power-law tails with a
Levy-type exponent , from which we derive the associated
break-even probability distribution. The predictions are compared with
empirical data.Comment: 6 pages, 6 figure
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