It is a common financial practice to estimate volatility
from the sum of frequently-sampled squared returns. However market
microstructure poses challenge to this estimation approach, as
evidenced by recent empirical studies in finance. This work
attempts to lay out theoretical grounds that reconcile continuous-time
modeling and discrete-time samples. We propose an estimation approach that
takes advantage of the rich sources in tick-by-tick data while
preserving the continuous-time assumption on the underlying
returns. Under our framework, it becomes clear why and where the ``usual''
volatility estimator fails when the returns are sampled at the highest
frequency.
Keywords: Measurement error; Subsampling; Market Microstructure;
Martingale; Bias-correction; Realized volatility