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on Market Microstructure |
| By: | Matej Steinbacher; Mitja Steinbacher; Matjaz Steinbacher |
| Abstract: | This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic bistability, which is not a result of randomness but an emergent property of micro-level trading rules, where even identical initial conditions lead to qualitatively different long-run price equilibria: a deterministic zero-price state and a persistent positive-price equilibrium. The study also identifies a metastable region with elevated volatility between the basins of attraction and reveals distinct transient behaviors for trajectories converging to these equilibria. Furthermore, we observe that the system is neither entirely regular nor fully chaotic. By highlighting the emergence of divergent market outcomes from uniform beginnings, this work contributes a novel perspective on the inherent path dependence and complex dynamics of artificial stock markets. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.17837 |
| By: | Mateusz Wilinski; Juho Kanniainen |
| Abstract: | In this work we show how generative tools, which were successfully applied to limit order book data, can be utilized for the task of imitating trading agents. To this end, we propose a modified generative architecture based on the state-space model, and apply it to limit order book data with identified investors. The model is trained on synthetic data, generated from a heterogeneous agent-based model. Finally, we compare model's predicted distribution over different aspects of investors' actions, with the ground truths known from the agent-based model. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.00982 |
| By: | Sergio Pulido (ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise, LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Mathieu Rosenbaum (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique); Emmanouil Sfendourakis (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Volume imbalance in a limit order book is often considered as a reliable indicator for predicting future price moves. In this work, we seek to analyse the nuances of the relationship between prices and volume imbalance. To this end, we study a market-making problem which allows us to view the imbalance as an optimal response to price moves. In our model, there is an underlying efficient price driving the mid-price, which follows the model with uncertainty zones. A single market maker knows the underlying efficient price and consequently the probability of a mid-price jump in the future. She controls the volumes she quotes at the best bid and ask prices. Solving her optimization problem allows us to understand endogenously the price-imbalance connection and to confirm in particular that it is optimal to quote a predictive imbalance. Our model can also be used by a platform to select a suitable tick size, which is known to be a crucial topic in financial regulation. The value function of the market maker's control problem can be viewed as a family of functions, indexed by the level of the market maker's inventory, solving a coupled system of PDEs. We show existence and uniqueness of classical solutions to this coupled system of equations. In the case of a continuous inventory, we also prove uniqueness of the market maker's optimal control policy. |
| Keywords: | Hamilton-Jacobi-Bellman equation, classical solutions, stochastic optimal control, optimal tick size, high-frequency market-making, volume imbalance, market microstructure |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04362236 |
| By: | Matej Steinbacher; Mitja Steinbacher; Matjaz Steinbacher |
| Abstract: | This study examines the impact of different computing implementations of clearing mechanisms on multi-asset price dynamics within an artificial stock market framework. We show that sequential processing of order books introduces a systematic and significant bias by affecting the allocation of traders' capital within a single time step. This occurs because applying budget constraints sequentially grants assets processed earlier preferential access to funds, distorting individual asset demand and consequently their price trajectories. The findings highlight that while the overall price level is primarily driven by macro factors like the money-to-stock ratio, the market's microstructural clearing mechanism plays a critical role in the allocation of value among individual assets. This underscores the necessity for careful consideration and validation of clearing mechanisms in artificial markets to accurately model complex financial behaviors. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.01683 |