A unified theory of order flow, market impact, and volatility
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915768334024704 |
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| author | Muhle-Karbe, Johannes Chahdi, Youssef Ouazzani Rosenbaum, Mathieu Szymanski, Grégoire |
| author_facet | Muhle-Karbe, Johannes Chahdi, Youssef Ouazzani Rosenbaum, Mathieu Szymanski, Grégoire |
| contents | We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it 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 $H_0$, which measures the persistence of the core flow. Specifically, the signed flow converges to the sum of a fractional process with Hurst index $H_0$ and a martingale, while the limiting traded volume is a rough process with Hurst index $H_0-1/2$. No-arbitrage constraints imply that volatility is rough, with Hurst parameter $2H_0-3/2$, and that the price impact of trades follows a power law with exponent $2-2H_0$. The analysis of signed order flow data yields an estimate $H_0 \approx 3/4$. This is not only consistent with the square-root law of market impact, but also turns out to match estimates for the roughness of traded volumes and volatilities remarkably well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A unified theory of order flow, market impact, and volatility Muhle-Karbe, Johannes Chahdi, Youssef Ouazzani Rosenbaum, Mathieu Szymanski, Grégoire Statistical Finance Probability Mathematical Finance Trading and Market Microstructure Applications 60F05, 60G22, 60G55, 62P05, 91G15, 91G80 We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it 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 $H_0$, which measures the persistence of the core flow. Specifically, the signed flow converges to the sum of a fractional process with Hurst index $H_0$ and a martingale, while the limiting traded volume is a rough process with Hurst index $H_0-1/2$. No-arbitrage constraints imply that volatility is rough, with Hurst parameter $2H_0-3/2$, and that the price impact of trades follows a power law with exponent $2-2H_0$. The analysis of signed order flow data yields an estimate $H_0 \approx 3/4$. This is not only consistent with the square-root law of market impact, but also turns out to match estimates for the roughness of traded volumes and volatilities remarkably well. |
| title | A unified theory of order flow, market impact, and volatility |
| topic | Statistical Finance Probability Mathematical Finance Trading and Market Microstructure Applications 60F05, 60G22, 60G55, 62P05, 91G15, 91G80 |
| url | https://arxiv.org/abs/2601.23172 |