"Power and bipower variation with stochastic volatility and jumps"
Ole E. Barndorff-Nielsen
The Centre for Mathematical Physics and Stochastics (MaPhySto),
University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark
and
Neil Shephard
Nuffield College, Oxford OX1 1NF, UK.
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.