The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market

The statistical properties of the Hang Seng index in the Hong Kong stock market are analyzed. The data include minute by minute records of the Hang Seng index from January 3, 1994 to May 28, 1997. The probability distribution functions of index returns for the time scales from 1 minute to 128 minutes are given. The results show that the nature of the stochastic process underlying the time series of the returns of Hang Seng index cannot be described by the normal distribution. It is more reasonable to model it by a truncated Lévy distribution with an exponential fall-off in its tails. The scaling of the maximium value of the probability distribution is studied. Results show that the data are consistent with scaling of a Lévy distribution. It is observed that in the tail of the distribution, the fall-off deviates from that of a Lévy stable process and is approximately exponential, especially after removing daily trading pattern from the data. The daily pattern thus affects strongly the analysis of the asymptotic behavior and scaling of fluctuation distributions. Received 9 August 2000 and Received in final form 28 August 2000     

Inverse statistics in the foreign exchange market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed by Simonsen et al. (Eur. Phys. J. 27 (2002) 583) and Jensen et al. (Physica A 324 (2003) 338). Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) ρ in the price of an investment. The analysis is performed for the Deutsch Mark (DM) against the US$ for the full year of 1998, but similar results are obtained for the Japanese Yen against the US$. With high statistical significance, the presence of “resonance peaks” in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the market participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new stylized fact, is observed for the (normalized) waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale-dependent features of the market activity.     

Non-homogeneous random walks, generalised master equations, fractional Fokker-Planck equations, and the generalised Kramers-Moyal expansion

A generalised random walk scheme for random walks in an arbitrary external potential field is investigated. From this concept which accounts for the symmetry breaking of homogeneity through the external field, a generalised master equation is constructed. For long-tailed transfer distance or waiting time distributions we show that this generalised master equation is the genesis of apparently different fractional Fokker-Planck equations discussed in literature. On this basis, we introduce a generalisation of the Kramers-Moyal expansion for broad jump length distributions that combines multiples of both ordinary and fractional spatial derivatives. However, it is shown that the nature of the drift term is not changed through the existence of anomalous transport statistics, and thus to first order, an external potential Φ(x) feeds back on the probability density function W through the classical term ∝/ x (x)W(x, t), i.e., even for Lévy flights, there exists a linear infinitesimal generator that accounts for the response to an external field. Received 30 June 2000 and Received in final form 12 November 2000     

Correlation structures in short-term variabilities of stock indices and exchange rates

Financial data usually show irregular fluctuations and some trends. We investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) among financial data from the viewpoint of deterministic dynamical systems. Our method is based on the small-shuffle surrogate method. The data we use are daily closing price of Standard & Poor's 500 and the volume, and daily foreign exchange rates, Euro/US Dollar (USD), British Pound/USD and Japanese Yen/USD. We found that these data are not independent.     

On entropy, financial markets and minority games

The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B—Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.     

The distribution of first-passage times and durations in FOREX and future markets

Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter t_max, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail.     

From market games to real-world markets

This paper uses the development of multi-agent market models to present a unified approach to the joint questions of how financial market movements may be simulated, predicted, and hedged against. We first present the results of agent-based market simulations in which traders equipped with simple buy/sell strategies and limited information compete in speculatory trading. We examine the effect of different market clearing mechanisms and show that implementation of a simple Walrasian auction leads to unstable market dynamics. We then show that a more realistic out-of-equilibrium clearing process leads to dynamics that closely resemble real financial movements, with fat-tailed price increments, clustered volatility and high volume autocorrelation. We then show that replacing the `synthetic' price history used by these simulations with data taken from real financial time-series leads to the remarkable result that the agents can collectively learn to identify moments in the market where profit is attainable. Hence on real financial data, the system as a whole can perform better than random. We then employ the formalism of Bouchaud in conjunction with agent based models to show that in general risk cannot be eliminated from trading with these models. We also show that, in the presence of transaction costs, the risk of option writing is greatly increased. This risk, and the costs, can however be reduced through the use of a delta-hedging strategy with modified, time-dependent volatility structure. Received 30 August 2000     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Studies on CdS nanoparticles dispersed in silica matrix prepared by sol-gel technique

SiO₂/CdS-nanoparticle composite films (SiO₂:CdS=85:15, 80:20, 75:25 and 70:30) were prepared by the sol-gel route. The films were characterized by studying microstructural (XRD and TEM) and optical (transmittance and photoluminescence) properties. Band gaps of these films annealed at different temperatures (373-473 K) for different times (10-120 min) indicated that the signature of nanocrystallinity is retained throughout the range of our experimental conditions. A thermal diffusion process controlled growth in the crystallite size with increasing annealing time and temperature. The average radii of the nanoparticles varied as the cube root of the annealing time but showed exponential dependence on the inverse of annealing temperature. Photoluminescence (PL) studies of the composite films indicated excitonic transitions. Theoretical analysis of the line shapes of the PL peaks recorded at 300 K and 80 K could be accounted for by the combined effects of size distribution and phonon broadening. It was observed that the deformation potential (E _d) effectively controlled the line shapes of the PL measurements. Received 24 May 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: msakp@mahendra.iacs.res.in     

Rheology and aging: A simple approach

We introduce a rheological model to describe the low-frequency mechanical properties of systems near a fluid/paste transition. We propose a Landau-like expansion for the vicinity of this transition, treating the stress relaxation rate as an order parameter. This leads to a formally simple model that allows us to describe the interplay between aging and non-linearities in the mechanical response of the system. We focus here on systems prepared by fluidification under a strong shear, on which mechanical measurments are performed (oscillatory rheology, stress relaxation, response to a steady shear rate), after a waiting time during which the system evolves on its own. Received 14 June 2000     

Broad distribution effects in sums of lognormal random variables

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out. Received 8 November 2002 / Received in final form 17 March 2003 Published online 7 May 2003     

Variable focal lens controlled by an external voltage: An application of electrowetting

We use electrocapillarity in order to change the contact angle of a transparent drop, thus realizing a lens of variable focal length (B. Berge, J. Peseux, Patent deposited in Grenoble France, October 8th 1997, numéro d'enregistrement national 97 12781). The key point is the application of gradients of wettability, which control the shape of the drop edge, in our case a centered circle of variable radius. The quality and reversibility of the lens are surprisingly good. The optical power variation can be 5 to 10 times the one of the human eye, for a comparable diameter, with a typical response time of 0.03 s and a dissipated power of a few mW. Received 1 December 1999     

Static and dynamic properties of supercooled thin polymer films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. An analysis of the temperature dependence of the α-relaxation time suggests that the critical temperature, T _c, of MCT decreases with D. If the confinement is not too strong ( D≥10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T _c(D), to the critical temperature. This suggests that T - T _c(D) is an important temperature scale of our model both in the bulk and in the films. Received 12 September 2001     

Hyperviscous diblock copolymer vesicles

Giant vesicles prepared from the diblock copolymer polybutadien-b-polyethyleneoxide (PB-PEO) exhibit a shear surface viscosity, which is about 500 times higher than those found in common phospholipid bilayers. Our result constitutes the first direct measurement of the shear surface viscosity of such polymersomes. At the same time, we measure bending and stretching elastic constants, which fall in the range of values typical for lipid membranes. Pulling out a tether from an immobilized polymersome and following its relaxation back to the vesicle body provides an estimate of the viscous coupling between the two monolayers composing the polymer membrane. The detected intermonolayer friction is about an order of magnitude higher than the characteristic one for phospholipid membranes. Polymersomes are tough vesicles with a high lysis tension. This, together with their robust rheological properties, makes them interesting candidates for a number of technological applications. Received 2 March 2001 and Received in final form 15 February 2002     

Scale-free behavior of the Internet global performance

Measurements and data analysis have proved very effective in the study of the Internet's physical fabric and have shown heterogeneities and statistical fluctuations extending over several orders of magnitude. Here we focus on the relationship between the Round-Trip-Time (RTT) and the geographical distance. We define dimensionless variables that contain information on the quality of Internet connections finding that their probability distributions are characterized by a slow power-law decay signalling the presence of scale-free features. These results point out the extreme heterogeneity of Internet delay since the transmission speed between different points of the network exhibits very large fluctuations. The associated scaling exponents appear to have fairly stable values in different data sets and thus define an invariant characteristic of the Internet that might be used in the future as a benchmark of the overall state of “health” of the Internet. Received 25 January 2003 Published online 7 May 2003     

Isovector deformation and its link to the neutron shell closure

DWBA analysis of the inelastic ^30-40S(p,p') and ^18-22O(p,p') scattering data measured in the inverse kinematics has been performed to determine the isoscalar (δ₀) and isovector (δ₁) deformation lengths of the 2⁺₁ excitations in the Sulfur and Oxygen isotopes using a compact folding approach. A systematic N-dependence of δ₀ and δ₁ has been established which shows a link between δ₁ and the neutron-shell closure. Strong isovector deformations were found in several cases, e.g., the 2⁺₁ state in ²⁰O where δ₁ is nearly three times larger than δ₀. These results confirm the relation δ₁>δ₀ anticipated from the core polarization by the valence neutrons in the open-shell (neutron rich) nuclei. The effect of neutron shell closure at N=14 or 16 has been discussed based on the folding model analysis of the inelastic ²²O+p scattering data at 46.6 MeV/u measured recently at GANIL.     

Acoustic emission from paper fracture

We report tensile failure experiments on paper sheets. The acoustic emission energy and the waiting times between acoustic events follow power-law distributions. This remains true while the strain rate is varied by more than 2 orders of magnitude. The energy statistics has the exponent beta approximately 1.25+/-0.10 and the waiting times the exponent tau approximately 1.0+/-0.1, in particular, for the energy roughly independent of the strain rate. These results do not compare well with fracture models, for (brittle) disordered media, which as such exhibit criticality. One reason may be residual stresses, neglected in most theories.     

Deuteron photodisintegration within the Quark-Gluon Strings Model and QCD motivated nonlinear Regge trajectories

We investigate deuteron two-body photodisintegration within the framework of the Quark-Gluon Strings Model with nonlinear baryon Regge trajectories. Special attention is paid to the use of QCD motivated Regge trajectories of the logarithmic and square-root form. We find that the recent experimental data from TJNAF in the few-GeV region can be reasonably described by the model. Angular distributions at different γ-energies are presented and the effect of a forward-backward asymmetry is discussed. Predictions for the energy dependence of dσ/dt at higher energies and different Θ_c.m. are presented, too. Received: 12 March 2001 / Accepted: 19 March 2001     

Treatment of kurtosis in financial markets

Since Mandelbrot (1963) [2] highlighted the fact that data on the yield of financial assets exhibit leptokurtosis, different distributions have been presented as alternatives to the normal distribution. So far little consideration has been given to the capacity that these distributions have to recover the kurtosis of the sample data. Our work aims to present distributions which, given the broad range of their kurtosis, have the capacity to perform adjustment on many occasions where other distributions fail, while also being capable of recovering the peakedness of the empirical data. Another key characteristic of these distributions is that they are defined within a bounded domain in the same way as the sample data. An empirical application of these distributions is presented within the financial field by using daily returns.