Microstructural Foundations for Rough Noise
Dr. Peter Korsbakke Christensen
Postdoctoral Researcher
Center for Research in Energy: Economics and Markets (CoRE) Aarhus University
Date: 1 August 2025 (Friday)
Time: 12:30-13:30
Venue: E22-4051
Host: Prof. Jun YU, UMDF Chair Professor of Finance and Economics, Chair Professor of Finance and Economics
Abstract
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 propose 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 a GMM estimation method applicable to tick-by-tick data, and develop a formal statistical test for the presence of rough noise. We show that the estimator and tests work in finite samples through a simulation study and apply it to tick-by-tick data on the INTC ticker. We confirm their finding that the roughness index has been close to zero in recent years. However, because our estimator is designed for tick-by-tick data, we are able to estimate the roughness index on a daily level, which reveals significant day-to-day variation in the roughness index.
Speaker
Peter Korsbakke Christensen is a postdoctoral researcher at the Center for Research in Energy: Economics and Markets (CoRE) at Aarhus University. He obtained his PhD from Aarhus University in 2024, with a thesis in high-frequency econometrics focusing on rough processes. His research interests include high-frequency econometrics, volatility modelling, and the dynamics of prices in energy markets.
All are welcome!
