Microstructure noise, realized volatility, and optimal sampling∗

Recorded prices are known to diverge from their “efficient” values due to the presence of market microstructure contaminations. The microstructure noise creates a dichotomy in the model-free estimation of integrated volatility. While it is theoretically necessary to sum squared returns that are computed over very small intervals to better indentify the underlying volatility over a period, the summing of numerous contaminated return data entails substantial accumulation of noise. We argue that the resulting effect is the determination of a bias/variance trade-off. We quantify the trade-off in the presence of a realistic microstructure model of price determination and provide clear and easily implementable directions for optimally sampling high frequency data for the purpose of volatility estimation. ∗Paper written for the CIRANO conference “Realized Volatility,” Montreal, November 7-8, 2003.