Power and Bipower Variation with Stochastic Volatility and Jumps

Abstract

This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models - thus providing a model free and consistent alternative to realised variance. Its robustness property means that if we have an SV plus infrequent jumps process then the difference between realised variance and realised bipower variation estimates the quadratic variation of the jump component. This seems to be the first method which can divide up quadratic variation into its continuous and jump components. Various extensions are given. Proofs of special cases of these results are given. Detailed mathematical results will be reported elsewhere.

Keywords: Bipower variation, Integrated variance, Jump process, Power variation, Quadratic variation, Realised variance, Realised volatility, Semimartingale, Volatility