2025/02/25 by Yuki Sato, Sato, Yuki, Kiyoshi Kanazawa +1 · 1 voice · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Physical sciences #Financial Markets and Investment Strategies #General Economics (econ.GN) #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Statistical Mechanics (cond-mat.stat-mech) #Trading and Market Microstructure (q-fin.TR) #cond-mat.stat-mech #econ.GN #q-fin.MF #q-fin.PR #q-fin.TR
paper · pdf · doi:10.48550/arxiv.2502.17906
openalex publication_date 2025/02/25 · arxiv published 2025/02/25 · arxiv updated 2025/05/27 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
In financial market microstructure, there are two enigmatic empirical laws: (i) the market-order flow has predictable persistence due to metaorder splitters by institutional investors, well formulated as the Lillo-Mike-Farmer model. However, this phenomenon seems paradoxical given the diffusive and unpredictable price dynamics; (ii) the price impact I(Q) of a large metaorder Q follows the square-root law, I(Q)∝ √(Q). Here we theoretically reveal why price dynamics follows Brownian motion despite predictable order flow by unifying these enigmas. We generalize the Lillo-Mike-Farmer model to nonlinear price-impact dynamics, which is mapped to an exactly solvable Lévy-walk model. Our exact solution shows that the price dynamics remains diffusive under the square-root law, even under persistent order flow. This work illustrates the crucial role of the square-root law in mitigating large price movements by large metaorders, thereby leading to the Brownian price dynamics, consistently with the efficient market hypothesis over long timescales.