Related papers: A Note on Jump Atlas Models
The vast majority of market impact studies assess each product individually, and the interactions between the different order flows are disregarded. This strong approximation may lead to an underestimation of trading costs and possible…
In this paper, we consider the drawdown and drawup of the fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in financial market. We derive the…
Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns…
This paper studies the time-varying structure of the equity market with respect to market capitalization. First, we analyze the distribution of the 100 largest companies' market capitalizations over time, in terms of inequality,…
We study the limit of the joint distribution of a multidimensional Generalized Tempered Stable (GTS) process and its quadratic covariation process when the stable index tends to two. Under a proper scaling, the GTS processes converges to a…
During training, weight matrices in machine learning architectures are updated using stochastic gradient descent or variations thereof. In this contribution we employ concepts of random matrix theory to analyse the resulting stochastic…
Brownian motion whose infinitesimal variance changes according to a three-state continuous time Markov Chain is studied. This Markov Chain can be viewed as a telegraph process with one on state and two off states. We first derive the…
By assuming the existence of the growth optimal portfolio (GOP), the stationarity of GOP-volatilities, and the maximization of relative entropy, the paper applies the benchmark approach to the modeling of the long-term dynamics of…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
In order to simulate the complex phenomena manifested in stock markets, we introduce a continuous asynchronous model in which millions of individual traders interact through a central orders matching mechanism, just as it happens in real…
We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function…
This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily…
Cascades of events and extreme occurrences have garnered significant attention across diverse domains such as financial markets, seismology, and social physics. Such events can stem either from the internal dynamics inherent to the system…
Equity activity is an essential topic for financial market studies. To explore its statistical regularities, we comprehensively examine the trading value, a measure of the equity activity, of the 3314 most-traded stocks in the U.S. equity…
Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high…
This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out…
We study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns. In these networks the nodes represent companies and links are related to the correlation coefficients between them.…
The capital asset pricing model (CAPM) is readily used to capture a linear relationship between the daily returns of an asset and a market index. We extend this model to an intraday high-frequency setting by proposing a functional CAPM…
We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning…
We demonstrate that future market correlation structure can be predicted with high out-of-sample accuracy using a multiplex network approach that combines information from social media and financial data. Market structure is measured by…