Estimating time-changes in noisy Lévy models
The Annals of Statistics · 2014 · Volume 42 · Issue 5
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.
Keywords
62G08, 62G20, 62G35, 62P20, Itô semimartingale, Lévy process, microstructure noise, time-change, Volatility
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