Estimating time-changes in noisy L\'evy models
In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility, obtaining convergence rates as good as any previously implied in the literature.
|Date of creation:||Dec 2013|
|Date of revision:||Nov 2014|
|Publication status:||Published in Annals of Statistics 2014, Vol. 42, No. 5, 2026-2057|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Peter Carr & Liuren Wu, 2002.
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- Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006.
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