A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

The price range, defined as the difference between the highest and lowest log asset prices over a fixed sampling interval (for concreteness, we focus on a 1-day interval), has a long, colorful, and distinguished history of use as a volatility estimator. As emphasized most recently by Alizadeh, Brandt, and Diebold (2002), the range is a highly efficient volatility proxy, distilling volatility information from the entire intraday price path, in contrast to volatility proxies based on the daily return, such as the daily squared return, which use only the opening and closing prices.Moreover, data on the