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

Bull, Adam D.

Ann. Stat. 42, No. 5, 2026-2057 (2014).

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

Keywords:

Itō semimartingale; Lévy process; microstructure noise; volatility; time-change