Open Access
Translator Disclaimer
October 2014 Estimating time-changes in noisy Lévy models
Adam D. Bull
Ann. Statist. 42(5): 2026-2057 (October 2014). DOI: 10.1214/14-AOS1250

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.

Citation

Download Citation

Adam D. Bull. "Estimating time-changes in noisy Lévy models." Ann. Statist. 42 (5) 2026 - 2057, October 2014. https://doi.org/10.1214/14-AOS1250

Information

Published: October 2014
First available in Project Euclid: 11 September 2014

zbMATH: 1305.62387
MathSciNet: MR3262476
Digital Object Identifier: 10.1214/14-AOS1250

Subjects:
Primary: 62P20
Secondary: 62G08 , 62G20 , 62G35

Keywords: Itô semimartingale , Lévy process , microstructure noise , time-change , Volatility

Rights: Copyright © 2014 Institute of Mathematical Statistics

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.42 • No. 5 • October 2014
Back to Top