Power and Bipower Variation with Stochastic Volatility and Jumps

This article shows that realized power variation and its extension,realized bipower variation, which we introduce here, are somewhatrobust to rare jumps. We demonstrate that in special cases,realized bipower variation estimates integrated variance instochastic volatility models, thus providing a model-free andconsistent alternative to realized variance. Its robustnessproperty means that if we have a stochastic volatility plusinfrequent jumps process, then the difference between realizedvariance and realized bipower variation estimates the quadraticvariation of the jump component. This seems to be the firstmethod that can separate quadratic variation into its continuousand jump components. Various extensions are given, togetherwith proofs of special cases of these results. Detailed mathematicalresults are reported in Barndorff-Nielsen and Shephard (2003a).