A semi-Markov model with memory for price changes

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov which depends also on a memory index. The index is introduced to take into account periods of high and low volatility in the market. First of all we derive the equations governing the process and then theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010

Controlled quantum evolutions and transitions

We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows to realize arbitrary evolutions ruled by these equations, to account for controlled quantum transitions. The method is illustrated by presenting the detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator. Possible extensions to anharmonic systems and mixed states are briefly discussed and assessed.Comment: 24 pages, 4 figure

A stochastic-hydrodynamic model of halo formation in charged particle beams

The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schr\"odinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasi-stationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.Comment: 18 pages, 20 figures, submitted to Phys. Rev. ST A

Stochastic collective dynamics of charged--particle beams in the stability regime

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by $\lambda_c\sqrt{N}$, where $N$ is the number of particles in the beam and $\lambda_c$ the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schr\"odinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so--called ``quantum--like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam--field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.Comment: 15 pages, 9 figure

Inverse Statistics in the Foreign Exchange Market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ 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 markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the 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.Comment: 8 pages. Accepted Physica

Price leadership and volatility linkages between oil and renewable energy firms during the covid-19 pandemic

The COVID-19 pandemic is shaving a strong influence in all areas of society, like wealth, economy, travel, lifestyle habits, and, amongst many others, financial and energy markets. The influence in standard energies, like crude oil, and renewable energies markets has been twofold: from one side, the predictability of volatility has strongly decreased; secondly, the linkages of the price time series have been modified. In this paper, by using DCC-GARCH and Price Leadership Share method-ology, we can investigate the changes in the influences between standard energies and renewable energies markets by analyzing one-minute time series of West Texas Intermediate crude oil futures contract (WTI), the Brent crude oil futures contract (BRENT), the STOXX Europe 600 oil & gas index (SXEV), and the European renewable energy index (ERIX). Our results confirm volatility spillover between the time series. However, when assessing the accuracy of the predictability of the DCC-GARCH model, the results show that the model fails its prediction in the period of higher instability. Besides, we found that price leadership has been strongly influenced by the virus spreading stages. These results have been obtained by dividing the period between September 2019 and January 2021 into 6 subperiods according to the pandemic stages

Weighted-indexed semi-Markov models for modeling financial returns

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010.Comment: arXiv admin note: substantial text overlap with arXiv:1109.425