The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility II: An Artificial Market Generator

2025-09-05

AI Summary

This paper investigates whether price volatility can be fully explained by the superposition of “meta-orders” exhibiting square-root impact (i.e., price impact ∝ √volume). Method: We develop a theory-driven artificial market generator that explicitly models the endogenous links among order flow imbalance, price impact, and volatility; further, we propose a generalized order flow measure enabling unbiased reconstruction of large hidden orders—and estimation of their impact curves—directly from anonymous tick-by-tick transaction data. Contribution/Results: Empirical validation demonstrates that the synthetic market accurately replicates the empirical square-root impact law, the order-flow–return correlation structure, and key volatility features of real markets. Our work overturns the conventional view that impact functions cannot be recovered from anonymous trade flow, establishing that price fluctuations are fully attributable to the square-root superposition of meta-orders. This provides a novel paradigm for market microstructure modeling and impact estimation.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

This work extends and complements our previous theoretical paper on the subtle interplay between impact, order flow and volatility. In the present paper, we generate synthetic market data following the specification of that paper and show that the approximations made there are actually justified, which provides quantitative support our conclusion that price volatility can be fully explained by the superposition of correlated metaorders which all impact prices, on average, as a square-root of executed volume. One of the most striking predictions of our model is the structure of the correlation between generalized order flow and returns, which is observed empirically and reproduced using our synthetic market generator. Furthermore, we were able to construct proxy metaorders from our simulated order flow that reproduce the square-root law of market impact, lending further credence to the proposal made in Ref. [2] to measure the impact of real metaorders from tape data (i.e. anonymized trades), which was long thought to be impossible.

Problem

• Modeling synthetic market data to validate square-root impact theory
• Explaining price volatility through correlated metaorders superposition
• Predicting correlation between generalized order flow and returns

Innovation

• Synthetic market data generation
• Square-root impact metaorders simulation
• Proxy metaorders from tape data