Estimating time-changes in noisy Lévy models. (English) Zbl 1305.62387

Summary: In quantitative finance, we often model asset prices as a noisy Itō 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.


62P20 Applications of statistics to economics
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
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