In recent years, there has been a substantive interest in rough volatility models. In this class
of models, the local behavior of stochastic volatility is much more irregular than …

We establish the weak convergence of the intensity of a nearly-unstable Hawkes process
with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market …

We consider the problem of estimating the roughness of the volatility in a stochastic volatility
model that arises as a nonlinear function of fractional Brownian motion with drift. To this end …

Starting from the notion of multivariate fractional Brownian Motion introduced in [F.
Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes …

We propose methods to infer jumps of a semi-martingale, which describes long-term price
dynamics based on discrete, noisy, high-frequency observations. Different to the classical …

We develop a nonparametric test for deciding whether volatility of an asset follows a
standard semimartingale process, with paths of finite quadratic variation, or a rough process …

This paper develops the fractional Bergomi model and introduces the two-factor fractional
Bergomi model with Hurst index H∈(0, 1 2). We examine both the existence and stability of …

This paper introduces a novel method for accurately approximating the spectral density of
the discretely-sampled fractional Ornstein-Uhlenbeck (fOU) process. We utilize this …

We propose a stochastic volatility model for time series of curves. It is motivated by dynamics
of intraday price curves that exhibit both between days dependence and intraday price …

The scope of this manuscript is to review some recent developments in statistics for
discretely observed semimartingales which are motivated by applications for financial …