Volatility and Covariation Estimation When Microstructure Noise and Trading Times Are Endogenous

This paper considers practically appealing procedures for estimating intraday volatility measures of financial assets. The underlying microstructure model accommodates the inherent properties of ultra high‐frequency data with the assumption of continuous efficient price processes. In this model, microstructure noise and trading times are endogenous but do not only depend on the prices. Using the (observed) last traded prices of the assets, we develop a new approach that enables to approximate the values of the efficient prices at some random times. Based on these approximated values, we build an estimator of the integrated volatility and give its asymptotic theory. We also give a consistent estimator of the integrated covariation when two assets (asynchronous by construction of the model) are observed.