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A unified theory of volume, volatility and impact

By Mathieu Rosenbaum

Appears in collection : COSA : Interactions in applied mathematics for economics, finance and Insurance / Interactions en mathématiques appliquées à l'économie, la finance et l'assurance

We propose a microstructural model for the order flow in financial markets that distinguishes between core orders and reaction flow, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a number of salient empirical properties: persistent signed order flow, rough trading volume and volatility, and power-law market impact.

In our framework, all these quantities are pinned down by a single statistic H0, which measures the persistence of the core flow. Specifically, the signed flow converges to the sum of a fractional process with Hurst index H0 and a martingale, while the limiting traded volume is a rough process with Hurst index H0 − 1/2.

No-arbitrage constraints imply that volatility is rough, with Hurst parameter 2H0 − 3/2, and that the price impact of trades follows a power law with exponent 2 − 2H0. The analysis of signed order flow data yields an estimate H0 close to 3/4.

Information about the video

Date of recording 14/09/2026
Date of publication 19/10/2026
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20533703
Cite this video Rosenbaum, Mathieu (14/09/2026). A unified theory of volume, volatility and impact. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20533703
URL https://dx.doi.org/10.24350/CIRM.V.20533703

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Bibliography

MUHLE-KARBE, Johannes, CHAHDI, Youssef Ouazzani, ROSENBAUM, Mathieu, et al. A unified theory of order flow, market impact, and volatility. arXiv preprint arXiv:2601.23172, 2026. - https://doi.org/10.48550/arXiv.2601.23172

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