Related papers: Two-sided estimates for stock price distribution d…
We derive the probability distribution of product of two independent random variables, each distributed according the one-dimensional stable law. We represent the density by its power series and its asymptotic expansions. As Fox's…
We study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…
We construct a two-tailed peak-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…
The percolation model of stock market speculation allows an asymmetry (in the return distribution) leading to fast downward crashes and slow upward recovery. We see more small upturns and more intermediate downturns.
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…
In this paper, we propose a new dynamical model to study the two-stage volatility evolution of stock market index after extreme events, and find that the volatility after extreme events follows a stretched exponential decay in the initial…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The…
We study the behaviour of a Brownian particle in the overdamped regime in the presence of a harmonic potential, assuming its diffusion coefficient to randomly jump between two distinct values. In particular, we characterize the probability…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
Information is a key component in determining the price of an asset in financial markets, and the main objective of this paper is to study the spread of information in this context. The network of interactions in financial markets is…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
We study the tails of closing auction return distributions for a sample of liquid European stocks. We use the stochastic call auction model of Derksen et al. (2020a), to derive a relation between tail exponents of limit order placement…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…