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

Abstract

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.

Published in at http://dx.doi.org/10.3150/08-BEJ167 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• Testing for jumps in a discretely observed process
• Realized range-based estimation of integrated variance

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