A tale of two time scales: Determining integrated volatility with noisy high frequency data
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.