An integrated cross-volatility estimation for asynchronous noisy data

Abstract

Let σ t be the instantaneous cross-volatility of two continuous semimartingales X and Y. In this paper, we introduce some estimators for the class of integrated cross-volatilities of the form where g is a continuous function and processes X and Y are sampled with microstructure noise and in an asynchronous way. In finance, it is widely accepted that the processes X and Y are reasonable models for the log return of price processes of stock and currency and our estimator is relevant in the context of intra-day high-frequency trading.