ESTIMATING TIME-CHANGES IN NOISY LEVY MODELS

• 成果类型: Article
• 署名作者: Bull, Adam D.
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1250
• 发表日期: 2014
• 页码: 2026-2057
• 关键词: nonparametric-estimation; INTEGRATED VOLATILITY; diffusion-coefficient; microstructure noise; efficient estimation; inference; jumps

摘要

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.