Jump Robust Volatility Estimation

We propose two new jump robust estimators of integrated variance based on high-frequency return observations. These MinRV and MedRV estimators provide a compelling alternative to the prevailing bi-power and multi-power variation measures. Specifically, the MedRV estimator has better theoretical efficiency properties than the tri-power variation measure and displays better finite-sample robustness to both jumps and the occurrence of “zero” returns in the sample. Unlike the bi-power variation measure the new estimator allows for the development of an asymptotic limit theory in the presence of jumps. Finally, it retains the local nature associated with the low order multi-power variation measures. This proves essential for avoiding the potential finite sample biases, arising from a pronounced intraday variation in the volatility level, that afflict alternative jump-robust integrated variance estimators based on longer blocks of returns. An empirical investigation of the Dow Jones 30 stocks as well as an extensive simulation study corroborate the theoretical robustness and efficiency properties of the new estimators. ∗Torben Andersen: Northwestern Univ.; NBER; CREATES; [email protected] Dobrislav Dobrev: Federal Reserve Board of Governors, [email protected] Ernst Schaumburg: Northwestern Univ., [email protected] We are grateful to Federico Bandi, Jean Jacod, Per Mykland, Roel Oomen, Mark Podolskij, Neil Shephard, Kevin Sheppard, Viktor Todorov, and Lan Zhang as well as conference participants at the Singapore Management University Conference in Honor of P.C.B. Phillips, July 2008 and the CREATES Volatility Symposium, Aarhus, August 2008 for their comments and suggestions. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Andersen gratefully acknowledges financial support from the NSF through a grant to the NBER and by CREATES funded by the Danish National Research Foundation.