Year: 2026
Type: article
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 optimisation 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.
Source: Finance and Stochastics
Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, École Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise, Laboratoire de Mathématiques et Modélisation d'Évry, École Polytechnique, Centre de Mathématiques Appliquées de l'École polytechnique, Institut Polytechnique de Paris
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $2,090
Funder: Université Paris-Saclay
OpenAlex ID: W7123659603