Asymptotic equivalence for inference on the volatility from noisy observations
The Annals of Statistics · 2011 · Volume 39 · Issue 2
Abstract
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam’s sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ and a nonstandard noise level. As an application, new rate-optimal estimators of the volatility function and simple efficient estimators of the integrated volatility are constructed.
Keywords
62B15, 62G20, 62M10, 91B84, diffusions with measurement error, equivalence of experiments, Gaussian shift, high-frequency data, integrated volatility, Le Cam deficiency, microstructure noise, spot volatility estimation
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