Measurement of Volatility of Diffusion Processes with Noisy High Frequency Data

A measurement volatility of return process should be the primary object of traders and practitioners in financial market for management of their portfolios and making trading decisions. The realized volatility is the representative estimator of (integrated) volatility and is computed from historical data of the return. The sampling interval of the return plays a key role in computing the realized volatility. It is commonly believed in empirical finance literature that the return process should not be sampled too often in a fixed period. The realized volatility results become biased if the sampling interval is chosen to be too small although the realized volatility computed from the high frequency data should be the reliable estimate from a statistical point of view.