Microstructural Foundations for Rough Noise

Christensen Peter, Aarhus University
Midtgaard Norlyk Anders, Aarhus University

Recently, it has been proposed to model the microstructure noise in prices by a continuous-time process with continuous sample paths that are rougher than those of a standard Brownian motion. In this paper, we provide a microstructural model for the tick-by-tick price changes that explicitly separates the permanent price changes from the fleeting price changes due to noise. We show how this model converges to a standard semimartingale model for the permanent price process, plus a rough noise term originating from the fleeting price changes on the macro scale. This provides a microstructural foundation for the rough-noise model, by explicitly documenting how this can arise from a realistic model for the noise in the tick-by-tick data. We then develop an estimation method applicable to tick-by-tick data and apply it to high-frequency data. In contrast to \cite{CDL2022}, we find that roughness is not a universal feature of the noise of asset prices, but rather seems to be linked to very active trading days.

Area: CS25 - Statistical analysis of high-frequency prices (Francesco Benvenuti)

Keywords: High frequency, rough processes, ambit stochastics, microstructure noise

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