Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps

Details Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps

2009-09-04

arxiv.org/abs/0909.0827v1

Bernoulli 2009, Vol. 15, No. 3, 634-658

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ167 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ167

We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower variation is proven. Under further assumptions we prove stable convergence of our estimates with the optimal rate $n^{-{1}/{4}}$. Moreover, we construct estimates which are robust to finite activity jumps.

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