Related papers: Volatility estimation in fractional Ornstein-Uhlen…
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…
In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the…
First-passage time (FPT) of an Ornstein-Uhlenbeck (OU) process is of immense interest in a variety of contexts. This paper considers an OU process with two boundaries, one of which is absorbing while the other one could be either reflecting…
We combine earlier investigations of linear systems with L\'{e}vy fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions of L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, (1999)]. We give a complete…
For a semi-martingale $X_t$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X, X \rangle_t$ is constructed based on observations in the vicinity of $X_t$. The problem is embedded in a…
We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of…
In Chen and Zhou 2021, they consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function…
We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by…
This study proposes a fast exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Lo\`eve expansions, the stochastic volatility path (Ornstein-Uhlenbeck process) is expressed as a sine…
We study a new measure of codependency in the second moment of a continuous-time multivariate asset price process, which we name the realized copula of volatility. The statistic is based on local volatility estimates constructed from…
We give an explicit representation for the transition law of a tempered stable Ornstein-Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation of increments from this process. Our results apply to…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…
In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…
The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion $B$ with Hurst index $H$. In the quadratic (resp. cubic) case, when $H<1/4$ (resp.…
We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…
We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary…