Related papers: The Microstructure of Stochastic Volatility Models…
Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…
Identifying the instances of jumps in a discrete-time-series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data…
We consider white noise perturbations of a nonlinear dynamical system in the neighborhood of an unstable critical point with linearization given by a Jordan block of full dimension. For the associated exit problem, we study the joint…
The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises.…
Generalized method of moments estimators based on higher-order moment conditions derived from independent shocks can be used to identify and estimate the simultaneous interaction in structural vector autoregressions. This study highlights…
Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock…
We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
While attention is a predictor for digital asset prices, and jumps in Bitcoin prices are well-known, we know little about its alternatives. Studying high frequency crypto data gives us the unique possibility to confirm that cross market…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…
This paper enhances the classical Solow model of economic growth by integrating L\'evy noise, a type of non-Gaussian stochastic perturbation, to capture the inherent uncertainties in economic systems. The extended model examines the impact…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
We focus on the influence of external sources of information upon financial markets. In particular, we develop a stochastic agent-based market model characterized by a certain herding behavior as well as allowing traders to be influenced by…
We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the…
Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic…
Using intraday data for the cross-section of individual stocks, we show that both transitory and persistent fluctuations in realized market and average idiosyncratic volatility, skewness and kurtosis are differentially priced in the…
We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [Bacry, Delattre, Hoffmann, Muzy, Modelling microstructure noise with…