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Nonlinear Connections Between Realized Volatility and High / Low Range Information

In this paper we look at the relationship between daily realized volatility estimates using intraday data and range based estimates using daily high/low price range information. Several classical range based volatility estimators are compared with nonlinear functional forms in mapping range based information onto realized volatility measures. We find that the older range based estimators can be improved by using more generalized nonlinear functions of the high/low range information. We show that these nonlinearities form an important piece of information for understanding the dynamics of prices at high frequencies. We also show that these improved volatility estimates can be used in forecasting future variances and risk measures, and improve on the typical range estimators.