Estimating time-changes in noisy L\'evy models
In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy 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.
|Date of creation:||Dec 2013|
|Date of revision:||Nov 2014|
|Publication status:||Published in Annals of Statistics 2014, Vol. 42, No. 5, 2026-2057|
|Contact details of provider:|| Web page: http://arxiv.org/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008.
"Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise,"
Econometric Society, vol. 76(6), pages 1481-1536, November.
- Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
- Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre.
- Carr, Peter & Wu, Liuren, 2004.
"Time-changed Levy processes and option pricing,"
Journal of Financial Economics,
Elsevier, vol. 71(1), pages 113-141, January.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1312.5911. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.