Volatility or microstructure noise?

The notion of realized volatility as a model-free measurement of the quadratic variation of the underlying log price process loses its asymptotic validity in the presence of market microstructure noise. Should microstructure contaminations be present, the summing of an increasing number of squared return data (as in the definition of the realized volatility estimator) simply entails increasing accumulation of noise. Using asymptotic arguments as in the extant theoretical literature on the subject, we show that the realized volatility estimator diverges to infinity almost surely when noise plays a role as in a realistic price formation mechanism. We also show that, while the quadratic variation of the log price process cannot be estimated consistently, an appropriately standardized version of the realized volatility estimator can be employed to uncover a specific feature of the noise distribution, namely the second moment of the noise process.