Estimating time-changes in noisy L\'evy models
Statistics Theory
2014-11-17 v5 Statistical Finance
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1312.5911,
title = {Estimating time-changes in noisy L\'evy models},
author = {Adam D. Bull},
journal= {arXiv preprint arXiv:1312.5911},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/14-AOS1250 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)