We consider a continuous semi-martingale sampled at hitting times of an irregular grid. The goal of this work is to analyze the asymptotic behavior of the realized volatility under this rather natural observation scheme. This framework strongly differs from the well understood situations when...

On consid`ere le mod`ele `a volatilit´e stochastique d´efini par les ´equations pr´ec´edentes,o`u B est un mouvement brownien et WH un mouvement brownien fractionnaire,ind´ependant de B, de param`etre de Hurst H 1/2. Ce mod`ele permet de reproduiredes propri´et´es de persistance dans la...

Weak dependence properties of ARCH-type bilinear models as introduced by Doukhanand Louhichi (1999) is investigated here. Those models are usually considered for their longrange dependence properties, see Giraitis and Surgailis (2002). Decay of the weak dependencecoefficient sequence are...

Based on the notion of first order dyadic p-variation, we give a new characterization of Besov spaces for 0<s<1, 1<=p,q<=+[infinity] and s>1/p. We also give results in the case where p1. Hence we provide simple tools that enable us to derive new regularity properties for the trajectories of various continuous time stochastic...</s<1,>

We introduce a new microstructure noise index for financial data. This index, the computation of which is based on the p-variations of the considered asset or rate at different time scales, can be interpreted in terms of Besov smoothness spaces. We study the behavior of our new index using...

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for continuous processes, we propose a framework enabling us...

We consider two continuous-time Gaussian processes, one being partially correlated to a time-lagged version of the other. We first give the limiting spectral distribution for the covariance matrices of the increments of the processes when the span between two observations tends to zero. Then, we...

We consider the stochastic volatility model with B a Brownian motion and [sigma] of the form where WH is a fractional Brownian motion, independent of the driving Brownian motion B, with Hurst parameter H=1/2. This model allows for persistence in the volatility [sigma]. The parameter of interest...

In practice, the choice of using a local volatility model or a stochastic volatility model is made according to their respective ability to fit implied volatility surfaces. In this paper, we adopt an opposite point of view. Indeed, based on historical data, we design a statistical procedure...

We provide asymptotic results for time-changed Lévy processes sampled at random instants. The sampling times are given by the first hitting times of symmetric barriers, whose distance with respect to the starting point is equal to [epsilon]. For a wide class of Lévy processes, we introduce a...