Fluctuations of trading volume in a stock market

We consider the probability distribution function of the trading volume and the volume changes in the Korean stock market. The probability distribution function of the trading volume shows double peaks and follows a power law, P(V/〈V〉)∼(V/〈V〉)^−α at the tail part of the distribution with α=4.15(4) for the KOSPI (Korea composite Stock Price Index) and α=4.22(2) for the KOSDAQ (Korea Securities Dealers Automated Quotations), where V is the trading volume and 〈V〉 is the monthly average value of the trading volume. The second peaks originate from the increasing trends of the average volume. The probability distribution function of the volume changes also follows a power law, , where V_r=V(t)−V(t−T) and T is a time lag. The exponents β depend on the time lag T. We observe that the exponents β for the KOSDAQ are larger than those for the KOSPI.     

A note on the sum of the sample autocorrelation function

It is shown that the sum of the sample autocorrelation function at lag h≥1 is always for any stationary time series with arbitrary length T≥2 (Hassani, 2009 [1]). In this paper, the distribution of a set of the sample autocorrelation function using the properties of this quantity is considered. It is found that the distribution of a set of the sample autocorrelation estimates is not independent and identically distributed. This finding implies that the result of diagnostic check and model building using the traditional assumption of iid can be quite misleading.     

Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained as timestep , which can be used as the actual price of an option. In fact, is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility to replace the volatility σ, where is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.     

Perturbation expansion for option pricing with stochastic volatility

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the same superposition of Black-Scholes expressions. An explicit analytic formula is deduced from a perturbation expansion around a Black-Scholes formula with the mean volatility. The expansion has two parts. The first takes into account the non-Gaussian character of the stock-fluctuations and is organized by powers of the excess kurtosis, the second is contract based, and is organized by the moments of moneyness of the option. With this expansion we show that for the Dow Jones Euro Stoxx 50 option data, a -hedging strategy is close to being optimal.     

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P_q(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution P_q(τ|τ₀), the mean conditional interval 〈τ|τ₀〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P_±(t) and find that P₋(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.     

Reverse Monte Carlo simulations and Raman scattering of an amorphous GeSe4 alloy produced by mechanical alloying

The short and intermediate range order of an amorphous GeSe₄ alloy produced by Mechanical Alloying were studied by Reverse Monte Carlo simulations of its X-ray total structure factor and Raman scattering. The simulations were used to compute the , and partial distribution functions and the , and partial structure factors. We calculated the coordination numbers and interatomic distances for the first and second neighbors. The data obtained indicate that the structure of the alloy has important differences when compared to alloys prepared by other techniques. There are a high number of Se-Se pairs in the first shell, and some of the tetrahedral units formed seemed to be connected by Se-Se bridges.     

Stock price fluctuations and the mimetic behaviors of traders

We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual market shows the power-law tail of the distribution of returns with the exponent outside the Levy stable region, the short memory of returns and the long memory of volatilities. The Hurst exponent of our model is asymptotically . An explanation is also given for the profile of the autocorrelation function, which is responsible for the value of the Hurst exponent.     

Identification of a rotator phase of octamethyl ferrocene and correlations between its structural and dynamical properties

The low- and high-temperature phases of octamethyl ferrocene were studied in detail, using high-resolution X-ray powder diffraction, differential scanning calorimetry and nuclear resonant scattering, in particular the novel technique of synchrotron radiation perturbed angular correlations (SRPAC). Much as in the case of an analogous but more unsymmetrical molecule, octamethyl ethinyl ferrocene, the high-temperature phase possesses the space group with lattice parameters , , which in the rhombohedral setting correspond to , α=104.79^°. An increase of the volume per formula unit of about 12% across the phase transition is observed.The rotation of the electric field gradient, which can be identified with the rotation of the entire molecule within the lattice, follows Arrhenius behaviour with a high activation energy of . Whereas precursor effects and a change in activation energy were observed for octamethyl ethinyl ferrocene, no such effects are observed for octamethyl ferrocene. We relate this difference to the absence of the ethinyl substituent in octamethyl ferrocene.     

The gated integration technique for the accurate measurement of the autocorrelation function of speckle intensities scattered from random phase screens

A new approach based on the gated integration technique is proposed for the accurate measurement of the autocorrelation function of speckle intensities scattered from a random phase screen. The Boxcar used for this technique in the acquisition of the speckle intensity data integrates the photoelectric signal during its sampling gate open, and it repeats the sampling by a preset number, m. The average analog of the m samplings output by the Boxcar enhances the signal-to-noise ratio by , because the repeated sampling and the average make the useful speckle signals stable, while the randomly varied photoelectric noise is suppressed by . In the experiment, we use an analog-to-digital converter module to synchronize all the actions such as the stepped movement of the phase screen, the repeated sampling, the readout of the averaged output of the Boxcar, etc. The experimental results show that speckle signals are better recovered from contaminated signals, and the autocorrelation function with the secondary maximum is obtained, indicating that the accuracy of the measurement of the autocorrelation function is greatly improved by the gated integration technique.     

Dispersive processes of light-induced defect creation in hydrogenated amorphous silicon

The growing curve of light-induced dangling bonds under illumination has been observed for various intensities of illumination in a-Si:H. It is fitted to a stretched exponential function and then two parameters β and τ involved in the function are estimated as a function of saturated dangling bond density . The experimental values of β, τ, and are compared with those calculated based on our model of light-induced defect creation in a-Si:H.     

Theoretical calculation of the isoelectronic line ratio of Li-like Ti and Cr under different mixture ratios

With the consideration of coronal conditions, a simplified model and the steady-state rate-equation are used to calculate the isoelectronic line ratio for transition in Li-like Ti and Cr from the electron temperature 400 to . The relation between the isoelectronic line ratio and the electron temperature are provided under different mixture ratios of Ti and Cr. Then, the mixture ratio from 2:1 to 3:1 between Ti and Cr are obtained that are suitable for the electron temperature diagnostic by using isoelectronic line ratio of Li-like Ti and Cr. The relative abundance of two close ionization stages, which is from bare nucleus to Be-like ionization stage, are given and show that the He-, Li- and Be-like are the principal ionization stages from 400 to for Ti and from 500 to for Cr. The Li-like charge state will reach the maximum distribution approximately from 400 to for Ti and from 547 to for Cr. The paper also shows that the dielectronic recombination and spontaneous radiative recombination rates only have small effects on the isoelectronic line ratio in the electron temperature 400-.     

First-principles study of arsenic impurity clusters in molecular beam epitaxy (MBE) grown HgCdTe

The understanding of the microstructures of the arsenic tetramer , dimer , and singlet of HgCdTe is important to explain the high electrical compensation of molecular beam epitaxy (MBE) samples and the conversion to p-type behavior. The stable configurations were obtained from the first-principles calculations for the arsenic cluster defects [ (n=1, 2, and 4)] in as-grown HgCdTe. According to the defect formation energies calculated under Te-rich conditions, the most probable configurations of , , and have been established. For the optimized and the energy is favorable to combine in a nearest neighboring mercury vacancy , and the corresponding configurations can be used to explain the self-compensated n-type characteristics in as-grown materials. is likely to be more abundant than in as-grown materials, but arsenic atoms are more strongly bounded in than in , thus more substantial activation energy is needed for than that for . The atomic relaxations as well as the structural stability of the arsenic defects have also been investigated.     

Synthesis of new La nitrides at high pressure and temperature

We have succeeded in synthesizing two new lanthanum nitrides in a supercritical nitrogen fluid at high pressure (about 30 GPa) and high temperature (about 2000 K), using a diamond anvil cell and a YAG laser heating system. These nitrides were found to be stable down to 5 GPa and ∼300 K in a nitrogen atmosphere. One of the new lanthanum nitrides is a cubic P lattice-type phase, which is a main phase synthesized nitride. The calculated lattice parameter is at 5 GPa, 300 K. The other nitride is of a trigonal P lattice-type. The calculated lattice parameters are and at 5 GPa, 300 K. The most likely phase of the former new La nitride is , the structure of which may be similar to the   Mn₂O₃-type (Ia80). The phase of the latter nitride is , the structure of which is the same as the   La₂O₃-type (hP5).     

Launch velocity characteristics of non-uniform sand in aeolian saltation

A numerical model for the vertical profile of aeolian mass flux was established based on the launch velocity probability distribution of saltating sand particles. The mean launch velocity () was used as a primary variable in the simulation, from which the average saltation height and length could be further calculated. The results showed that the mean launch velocity, the average saltation height, and the average saltation length increased with increasing wind friction velocity (u∗), although the increases for the first two were not significant. On the other hand, the relative mean launch velocity () was found to decrease with increasing wind friction velocity. Other interesting results were obtained from the simulation: both and decreased with an increase in the sand grain size, which agreed with a previous report claiming that the launch velocity was limited by the inertia of bed grains. Furthermore, decreasing dependence of the average saltation height and length was also found with increasing sand grain size. Overall, the sand grain size was of significance to the determination of probability distribution of the launch velocity and thus the saltation characteristics.     

Quantum critical behaviour in doped Y bB12 studied by ab initio calculations

The Kondo insulator Y bB₁₂ is known to undergo a transition to the metallic state with doping or under an external magnetic field. Within the virtual crystal approximation (VCA), we calculated the occupation of the Yb 4f and 5d shells, and , as a function of doping of Y bB₁₂ with the rare earths Tm and Lu. We found that exhibits an anomalous change at the critical concentration of the dopant, in agreement with experiment ( for Y b_1−xLu_xB₁₂ and for Y b_1−xTm_xB₁₂). We suggest that the critical behaviour seems to be strictly connected with the change of and in consequence the change of the Yb valency.     

The effect of the Bi source on optical properties of Bi2Te3 nanostructures

nanostructures were synthesized by using different Bi sources via a simple solvothermal process, in which and BiCl₃ were used as the Bi sources. Optical properties of nanostructures prepared with and BiCl₃ as the Bi sources were investigated by micro-Raman spectroscopy. The Raman scattering spectrum of hexagonal nanoplates prepared by using as the Bi source shows that the infrared (IR) active mode A_1u, which must be odd parity and is Raman forbidden for bulk crystal due to its inversion symmetry, is greatly activated and shows up clearly in the Raman scattering spectrum. We attribute the appearance of the infrared active A_1u mode in the Raman spectrum to crystal symmetry breaking of hexagonal nanoplates. However, the Raman scattering spectrum of nanostructures with irregular shape prepared by using as the Bi source only exhibits the two characteristic Raman modes of crystals. Micro-Raman measurements on nanostructures with different morphologies offer us a potential way to tailor optical properties of nanostructures by controlling the morphologies of the nanostructures, which is very important for practical applications of nanostructures in thermoelectric devices.     

Anomalous thermostat and intraband discrete breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. The coupling between both parts is bilinear. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation with memory kernels and noise term for the anharmonic coordinates . For zero temperature, i.e. for , we prove that the support of the Fourier transform of and of the time averaged velocity-velocity correlation functions of the anharmonic system cannot overlap. As a consequence, the asymptotic solutions can be constant, periodic, quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy E_T transferred to the harmonic system up to time T is proportional to T^α. If equals one of the phonon frequencies ω_ν, it is α=2. We prove that there is a zero measure set L such that for in its full measure complement R?L, it is α=0, i.e. there is no energy dissipation. Under certain conditions L contains a subset L^′ such that for the dissipation rate is nonzero and may be subdissipative (0≤α<1) or superdissipative (1<α≤2), compared to ordinary dissipation (α=1). Consequently, the harmonic bath does act as an anomalous thermostat, in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation, forcing convergence to equilibrium. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a Cantor set C(k) of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing for , related to . For the small denominators do not lead to divergencies such that is a smooth and bounded function in t.