The Annals of Statistics

Estimating time-changes in noisy Lévy models

Adam D. Bull

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 11 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.aos/1410440633

Digital Object Identifier
doi:10.1214/14-AOS1250

Mathematical Reviews number (MathSciNet)
MR3262476

Zentralblatt MATH identifier
1305.62387

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

Keywords
Itô semimartingale Lévy process microstructure noise volatility time-change

Citation

Bull, Adam D. Estimating time-changes in noisy Lévy models. Ann. Statist. 42 (2014), no. 5, 2026--2057. doi:10.1214/14-AOS1250. https://projecteuclid.org/euclid.aos/1410440633


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