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Title: Understanding the distribution of volatility Authors:  Martin Thyrsgaard - Aarhus University (Denmark) [presenting]
Kim Christensen - Aarhus University (Denmark)
Bezirgen Veliyev - Aarhus University (Denmark)
Abstract: A noise robust estimator is constructed for the cumulative distribution function of the invariant distribution of the latent spot volatility process of an asset price. As a first step towards constructing this estimator, we derive a noise robust estimator of the volatility occupation time over a fixed time span. This step relies on the asset price being observed over a grid with mesh going to zero. Noise robust estimators typically converge at a slower rate, however, a Monte Carlo study suggests that this cost is greatly outweighed by the benefits from being able to use more observations. In the second step, we let the time span tend to infinity while still letting the distance between observations tend to zero, thereby obtaining a consistent estimator of the cumulative distribution function of the invariant distribution. We use this estimator to construct a Kolmogorov-Smirnov type test for the invariant distribution of the latent volatility process. Finally, we apply the newly developed methods to a set of ultra high-frequency equity tick data.