Related papers: Are all highly liquid securities within the same c…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…
We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our…
This paper summarizes the properties of strongly correlating liquids, i.e., liquids with strong correlations between virial and potential energy equilibrium fluctuations at constant volume. We proceed to focus on the experimental…
This research presents a comprehensive framework for analyzing liquidity in financial markets, particularly in the context of high-frequency trading. By leveraging advanced machine learning classification techniques, including Logistic…
We introduce a class of stochastic volatility models $(X_t)_{t \geq 0}$ for which the absolute moments of the increments exhibit anomalous scaling: $\E\left(|X_{t+h} - X_t|^q \right)$ scales as $h^{q/2}$ for $q < q^*$, but as $h^{A(q)}$…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
A phenomenon of the financial log-periodicity is discussed and the characteristics that amplify its predictive potential are elaborated. The principal one is self-similarity that obeys across all the time scales. Furthermore the same…
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with…
Event-by-event fluctuations of the initial transverse density profile result in a collective flow pattern which also fluctuates event by event. We propose a number of new correlation observables to characterize these fluctuations and…
In this note, we consider European options of type $h(X^1_T, X^2_T,\ldots, X^n_T)$ depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between…
Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective…
The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous…
The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the…
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a…
Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the…