Related papers: Q-Gaussian diffusion in stock markets
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and…
We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and…
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…
The return distributions of the coherent noise model are studied for the system size independent case. It is shown that, in this case, these distributions are in the shape of q-Gaussians, which are the standard distributions obtained in…
In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model…
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…
The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact long term historical moments, is often…
In this paper, we establish a link between quantum stochastic processes, and nonlocal diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, 'The Quantum Black-Scholes…
We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock…
The market efficiency hypothesis has been proposed to explain the behavior of time series of stock markets. The Black-Scholes model (B-S) for example, is based on the assumption that markets are efficient. As a consequence, it is…
We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…
We provide evidence that cumulative distributions of absolute normalized returns for the $100$ American companies with the highest market capitalization, uncover a critical behavior for different time scales $\Delta t$. Such cumulative…
In this paper we study the distribution of a product of two continuous random variables. We derive formulas for the probability density functions and moments of the products of the Gaussian, log-normal, Student's t and Pareto random…
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…