<Para ID="Par1">We introduce a unifying class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed...</para>

We introduce a nonparametric estimator of the volatility function in univariate processes with Lévy type jumps and stochastic volatility when we observe the state variable at discrete times. Our results rely on the fact that it is possible to recognize the discontinuous part of the state...

We reconstruct the level-dependent diffusion coefficient of a univariate semimartingale with jumps which is observed discretely. The consistency and asymptotic normality of our estimator are provided in the presence of both finite and infinite activity (finite variation) jumps. Our results rely...

In this paper we consider two processes driven by Brownian motions plus drift and jumps with infinite activity. Given discrete observations on a finite time horizon, we study the truncated (threshold) realized covariance \hat{IC} to estimate the integrated covariation IC between the two Brownian...

We show that the Truncated Realized Variance (TRV) of a semimartingale asset price converges to zero when observations are contaminated by microstructure noises. Under the additive iid noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible...

We introduce a class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed...

We show that the Truncated Realized Variance (TRV) of a SemiMartingale (SM) converges to zero when observations are contaminated by noise. Under the additive i.i.d. noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible test allowing us to...

When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the <italic>integrated covariation</italic> (IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed...

In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the Threshold estimator is able to separate the integrated variance IV from the sum of...