×

Estimating time-changes in noisy Lévy models. (English) Zbl 1305.62387

Summary: In quantitative finance, we often model asset prices as a noisy Itō 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.

MSC:

62P20 Applications of statistics to economics
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
PDF BibTeX XML Cite
Full Text: DOI arXiv