共查询到20条相似文献,搜索用时 15 毫秒
1.
G.-F. Gu W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(4):585-592
Recently, Mike and Farmer have constructed a very powerful
and realistic behavioral model to mimick the dynamic process of
stock price formation based on the empirical regularities of order
placement and cancelation in a purely order-driven market, which can
successfully reproduce the whole distribution of returns, not only
the well-known power-law tails, together with several other
important stylized facts. There are three key ingredients in the
Mike-Farmer (MF) model: the long memory of order signs characterized
by the Hurst index Hs, the distribution of relative order prices
x in reference to the same best price described by a Student
distribution (or Tsallis’ q-Gaussian), and the dynamics of order
cancelation. They showed that different values of the Hurst index
Hs and the freedom degree αx of the Student distribution
can always produce power-law tails in the return distribution
fr(r) with different tail exponent αr. In this paper, we
study the origin of the power-law tails of the return distribution
fr(r) in the MF model, based on extensive simulations with
different combinations of the left part L(x) for x < 0 and the
right part R(x) for x > 0 of fx(x). We find that power-law
tails appear only when L(x) has a power-law tail, no matter R(x)
has a power-law tail or not. In addition, we find that the
distributions of returns in the MF model at different timescales can
be well modeled by the Student distributions, whose tail exponents
are close to the well-known cubic law and increase with the
timescale. 相似文献
2.
We study dynamical behavior of the Chinese stock markets by investigating the statistical properties of daily ensemble return and variety defined, respectively, as the mean and the standard deviation of the ensemble daily price return of a portfolio of stocks traded in China's stock markets on a given day. The distribution of the daily ensemble return has an exponential form in the center and power-law tails, while the variety distribution is lognormal in the bulk followed by a power-law tail for large variety. Based on detrended fluctuation analysis, R/S analysis and modified R/S analysis, we find evidence of long memory in the ensemble return and strong evidence of long memory in the evolution of variety. 相似文献
3.
Marcin Magdziarz Sebastian Orzeł Aleksander Weron 《Journal of statistical physics》2011,145(1):187-203
The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension
of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property
is manifested by the random (infinitely divisible) periods of time, during which the asset price does not change. We introduce
a subdiffusive arithmetic Brownian motion as a model of stock prices with such characteristics. The structure of this process
agrees with two-stage scenario underlying the anomalous diffusion mechanism, in which trapping random events are superimposed
on the Langevin dynamics. We find the corresponding fractional Fokker-Planck equation governing the probability density function
of the introduced process. We construct the corresponding martingale measure and show that the model is incomplete. We derive
the formulas for European put and call option prices. We describe explicit algorithms and present some Monte-Carlo simulations
for the particular cases of α-stable and tempered α-stable distributions of waiting times. 相似文献
4.
F. Lillo R.N. Mantegna 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(4):603-606
We select the n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We study the ensemble return distribution for each trading
day and we find that the symmetry properties of the ensemble return distribution drastically change in crash and rally days
of the market. In crash and rally days, the distribution becomes asymmetric. In particular for crashes the positive tail is
steeper than the negative one whereas the reverse is observed in rally days.
Received 25 February 2000 相似文献
5.
Jin-Rong Liang Jun Wang Long-Jin Lǔ Hui Gu Wei-Yuan Qiu Fu-Yao Ren 《Journal of statistical physics》2012,146(1):205-216
In statistical physics, anomalous diffusion plays an important role, whose applications have been found in many areas. In
this paper, we introduce a composite-diffusive fractional Brownian motion X
α,H
(t)=X
H
(S
α
(t)), 0<α,H<1, driven by anomalous diffusions as a model of asset prices and discuss the corresponding fractional Fokker-Planck equation
and Black-Scholes formula. We obtain the fractional Fokker-Planck equation governing the dynamics of the probability density
function of the composite-diffusive fractional Brownian motion and find the Black-Scholes differential equation driven by
the stock asset X
α,H
(t) and the corresponding Black-Scholes formula for the fair prices of European option. 相似文献
6.
Blinking of single molecules and nanocrystals is modeled as a two-state renewal process with on (fluorescent) and off (non-fluorescent)
states. The on and off-times may have power-law or exponential distributions. A fractional generalization of the exponential
function is used to develop a unified treatment of the blinking statistics for both types of distributions. In the framework
of the two-state model, an equation for the probability density p(t
on|t) of the total on-time is derived. As applied to power-law blinking, the equation contains derivatives of fractional orders
α and β equal to the exponents of the on and off-time power-law distributions, respectively. In the limit case of α = β =
1, the distributions become exponential and the fractional differential equation reduces to an integer order differential
equation. Solutions to these equations are expressed in terms of fractional stable distributions. The Poisson transform of
p(t
on|t) is the photon number distribution that determines the photon counting statistics. It is shown that the long-time asymptotic
behavior of Mandel’s Q parameter follows a power law: M(t) ∝ t
γ
. The function γ(α, β) is defined on the (α, β) plane. An analysis of the relative variance of the total on-time shows that it decays only
when α = β = 1 or α < β. Otherwise, relative fluctuations either exhibit asymptotic power-law growth or approach a constant
level. Analytical calculations are in good agreement with the results of Monte Carlo simulations. 相似文献
7.
8.
F.A.B.F. de Moura F. Domínguez-Adame 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(2):165-169
We study the nature of the vibrational modes in a two-dimensional harmonic
lattice with long-range correlated random masses, with power-law spectral
density S(k)∼1/kα. We obtain numerically the scale invariance of
the fluctuations of the relative participation number and the local density of
states. We find signatures of extended vibrational modes when α>αc
and αc depends on the magnitude of disorder. In order to confirm this
claim, we also study the time evolution of an initially localized perturbation
of the lattice. We show that the second moment of the spatial distribution of
the energy displays a ballistic regime when α>αc, in agreement with
the occurrence of extended vibrational modes. 相似文献
9.
W.-S. Jung F. Z. Wang S. Havlin T. Kaizoji H.-T. Moon H. E. Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(1):113-119
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the
Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated
by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects
such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution
and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical
features appear in different financial markets. We also compare our results between the period before and after the big crash
at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical
properties of the returns are different. 相似文献
10.
I.M. Sokolov 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(3):369-373
We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v
2(r) ∝r
α and the corresponding correlation time scales as τ(r) ∝r
β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 +
β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 +
β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation.
In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather
ballistic.
Received 13 March 2001 相似文献
11.
This study investigates the presence of deterministic dependencies in international stock markets using recurrence plots and recurrence quantification analysis (RQA). The results are based on a large set of free float-adjusted market capitalization stock indices, covering a period of 15 years. The statistical tests suggest that the dynamics of stock prices in emerging markets is characterized by higher values of RQA measures when compared to their developed counterparts. The behavior of stock markets during critical financial events, such as the burst of the technology bubble, the Asian currency crisis, and the recent subprime mortgage crisis, is analyzed by performing RQA in sliding windows. It is shown that during these events stock markets exhibit a distinctive behavior that is characterized by temporary decreases in the fraction of recurrence points contained in diagonal and vertical structures. 相似文献
12.
The dynamics of a flat isotropic brane Universe with two-component matter source —perfect fluid with the equation of statep = (γ − 1)ρ and a scalar field with a power-law potentialV ∼ φα is investigated. We describe solutions for which the scalar field energy density scales as a power-law of the scale factor.
We also describe solutions existing in regions of the parameter space where these scaling solutions are unstable or do not
exist. 相似文献
13.
L. G. Moyano A. P. Majtey C. Tsallis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(4):493-500
We introduce, and numerically study, a system of N symplectically and globally coupled
standard maps localized in a d=1 lattice array. The global coupling is modulated
through a factor r-α, being
r the distance between maps. Thus, interactions are long-range (nonintegrable) when
0≤α≤1, and short-range (integrable) when α>1.
We verify that the largest Lyapunov exponent λM scales as λM ∝
N-κ(α), where κ(α) is positive when interactions are
long-range, yielding weak chaos in the thermodynamic
limit N↦∞ (hence λM→0). In the short-range case,
κ(α) appears to vanish,
and the behaviour corresponds to strong chaos. We show that, for certain
values of the control parameters of the system, long-lasting metastable states
can be present. Their duration tc scales as tc ∝Nβ(α),
where β(α) appears to be numerically in agreement with the following
behavior: β>0 for 0 ≤α< 1, and zero for α≥1.
These results are consistent with features typically found in nonextensive statistical mechanics.
Moreover, they exhibit strong similarity between the present
discrete-time system, and the α-XY Hamiltonian ferromagnetic model. 相似文献
14.
Markus Heydenreich Remco van der Hofstad Akira Sakai 《Journal of statistical physics》2008,132(6):1001-1049
We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion
we prove mean-field behavior for these models if d>2(α
∧2) for self-avoiding walk and the Ising model, and d>3(α
∧2) for percolation, where d denotes the dimension and α the power-law decay exponent of the coupling function. We provide a simplified analysis of the lace expansion based on the
trigonometric approach in Borgs et al. (Ann. Probab. 33(5):1886–1944, 2005).
相似文献
15.
Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called “exactness of the mean-field theory”. It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the α-Potts model with annealed vacancies and the α-Potts model with invisible states. 相似文献
16.
L. Y. Gong P. Q. Tong Z. C. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,77(3):413-417
We study the von Neumann entropy and related quantities
in one-dimensional electron systems with on-site long-range
correlated potentials. The potentials are characterized by a
power-law power spectrum S(k) μ\propto 1/k
α, where α
is the correlation exponent. We find that the first-order
derivative of spectrum-averaged von Neumann entropy is maximal at
a certain correlation exponent α
m
for a finite system, and
has perfect finite-size scaling behaviors around α
m
. It
indicates that the first-order derivative of the spectrum-averaged
von Neumann entropy has singular behavior, and α
m
can be
used as a signature for transition points. For the infinite
system, the threshold value α
c
= 1.465 is obtained by
extrapolating α
m
. 相似文献
17.
We show that electron transport through a long multichannel wire, connected to leads by tunnel junctions, at low temperatures
T and voltages V is dominated by inelastic cotunneling. This mechanism results in experimentally observed power-law dependence of conductance
on T and V, in the diffusive regime where usual Coulomb anomaly theory leads to exponentially low conductance. The power-law exponent
α* is proportional to the distance between contacts L.
The article is published in the original. 相似文献
18.
We apply the universal properties with Gaussian orthogonal ensemble (GOE) of random matrices namely spectral properties, distribution of eigenvalues, eigenvalue spacing predicted by random matrix theory (RMT) to compare cross-correlation matrix estimators from emerging market data. The daily stock prices of the Sri Lankan All share price index and Milanka price index from August 2004 to March 2005 were analyzed. Most eigenvalues in the spectrum of the cross-correlation matrix of stock price changes agree with the universal predictions of RMT. We find that the cross-correlation matrix satisfies the universal properties of the GOE of real symmetric random matrices. The eigen distribution follows the RMT predictions in the bulk but there are some deviations at the large eigenvalues. The nearest-neighbor spacing and the next nearest-neighbor spacing of the eigenvalues were examined and found that they follow the universality of GOE. RMT with deterministic correlations found that each eigenvalue from deterministic correlations is observed at values, which are repelled from the bulk distribution. 相似文献
19.
G. Oh C. Eom F. Wang W.-S. Jung H. E. Stanley S. Kim 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,79(1):55-60
We investigate the statistical properties of the cross-correlation
matrix between individual stocks traded in the Korean stock market
using the random matrix theory (RMT) and observe how these affect
the portfolio weights in the Markowitz portfolio theory. We find
that the distribution of the cross-correlation matrix is positively
skewed and changes over time. We find that the eigenvalue
distribution of original cross-correlation matrix deviates from the
eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues
predicted by the RMT. The b473\beta_{473} coefficient, which reflect
the largest eigenvalue property, is 0.8, while one of the
eigenvalues in the RMT is approximately zero. Notably, we show
that the entropy function E(s)E(\sigma) with the portfolio risk
σ for the original and filtered cross-correlation matrices are
consistent with a power-law function, E(σ) ~
s-g\sigma^{-\gamma}, with the exponent γ ~ 2.92 and those for Asian currency crisis decreases significantly. 相似文献
20.
J. Healy M. Dixon B. Read F.F. Cai 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(2):219-227
We investigate what can be learned from a purely phenomenological study of options prices without modelling assumptions. We
fitted neural net (NN) models to LIFFE “ESX” European style FTSE 100 index options using daily data from 1992 to 1997. These
non-parametric models reproduce the Black-Scholes (BS) analytic model in terms of fit and performance measures using just
the usual five inputs (S, X, t, r, IV). We found that adding transaction costs (bid-ask spread) to these standard five parameters gives a comparable fit and
performance. Tests show that the bid-ask spread can be a statistically significant explanatory variable for option prices.
The difference in option prices between the models with transaction costs and those without ranges from about -3.0 to +1.5
index points, varying with maturity date. However, the difference depends on the moneyness (S/X), being greatest in-the-money.
This suggests that use of a five-factor model can result in a pricing difference of up to £10 to £30 per call option contract
compared with modelling under transaction costs. We found that the influence of transaction costs varied between different
yearly subsets of the data. Open interest is also a significant explanatory variable, but volume is not.
Received 31 December 2001 相似文献