In quantitative finance, we often model asset prices as a noisy Itô semimartingale. As this model is not identifiable, approximating by a time-changed Lévy 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.
"Estimating time-changes in noisy Lévy models." Ann. Statist. 42 (5) 2026 - 2057, October 2014. https://doi.org/10.1214/14-AOS1250