It is a common practice in finance to estimate volatility from the sum of frequently-sampled squared returns.However market microstructure poses challenges 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.
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