Capturing Volatility from Large Price Moves: Generalized Range Theory and Applications

I introduce a novel high-frequency volatility estimator based on large price moves, which constitutes a generalization of the range. Just like the standard range maximizes a single price di erence on the observed price path, the generalized range maximizes the sum of multiple price di erences. It provides a new link between recent advances in high-frequency volatility estimation and the long-established e ciency of the range. I develop an asymptotic theory for the generalized range in a jump-di usion setting, originating a family of strongly consistent di usive volatility estimators that are robust to jumps. This theory tackles maximization on a time grid not previously studied in the volatility literature and uncovers valuable distributional properties of price peaks and troughs. On simulated data, the generalized range behaves in accordance with the derived theory and compares favorably to other known estimators of di usive volatility that are robust to jumps. On real data, the generalized range is largely robust to microstructure noise when calculated on bid-ask quotes and proves valuable for intraday jump detection and short-term forecasting of stock return volatility. In a model-free environment, the capability of the generalized range to identify large zig-zag price moves appears to be directly applicable to relative value arbitrage strategies. yDepartment of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208, Tel.: +1 224 392 0782; Email: d-dobrev@kellogg.northwestern.edu I would like to thank Torben Andersen, Ravi Jagannathan, Robert McDonald, and Ernst Schaumburg for many helpful discussions and suggestions. I am grateful for valuable remarks also to Luca Benzoni, Oleg Bondarenko, Robert Korajczyk, Jacobs Sagi, Costis Skiadas, Arne Staal, Rakesh Vohra as well as seminar participants at Barclays Global Investors, Board of Governors of the Federal Reserve System, Carnegie Mellon University, Federal Reserve Bank of Boston, Federal Reserve Bank of Chicago, Lehman Brothers, Northwestern University, University of Chicago, University of Michigan, and 2006 CIREQ Conference on Realized Volatility. All errors and omissions are my own.