This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise, which are observed at high frequency. Our method generalizes the pre-averaging approach (see [13],[11]) and provides consistent estimates for various characteristics of general...

In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high...

This paper considers the problem of estimating spot volatility in the simultaneous presence of Lévy jumps and market microstructure noise. We propose to use the pre-averaging approach and the threshold kernel-based method to construct a spot volatility estimator, which is robust to both...

This article examines option pricing performance using realized volatilities with or without handling microstructure noise, non-trading hours and large jumps. The dynamics of realized volatility is specified by ARFIMA(X) and HAR(X) models. Main results using put options on the Nikkei 225 index...

We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous. The central limit theorem is shown to have a feasible version. In the process, we show that the...