The Annals of Statistics

Estimating time-changes in noisy Lévy models

Adam D. Bull

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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.

Article information

Ann. Statist., Volume 42, Number 5 (2014), 2026-2057.

First available in Project Euclid: 11 September 2014

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Zentralblatt MATH identifier

Primary: 62P20: Applications to economics [See also 91Bxx]
Secondary: 62G08: Nonparametric regression 62G20: Asymptotic properties 62G35: Robustness

Itô semimartingale Lévy process microstructure noise volatility time-change


Bull, Adam D. Estimating time-changes in noisy Lévy models. Ann. Statist. 42 (2014), no. 5, 2026--2057. doi:10.1214/14-AOS1250.

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