A mathematical framework for modelling order book dynamics

Rama Cont, Pierre Degond () and Xuan Lifan
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Rama Cont: University of Oxford
Pierre Degond: IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique
Xuan Lifan: Imperial College London

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Abstract: We present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a deterministic 'mass transport' operator acting on distributions of buy and sell orders. At the mathematical level, this corresponds to a natural decomposition of the infinitesimal generator describing the evolution of the limit order book into two operators: the generator of the order flow and the clearing operator. Our model provides a flexible framework for modelling and simulating order book dynamics and studying various scaling limits of discrete order book models. We show that our framework includes previous models as special cases and yields insights into the interplay between order flow and price dynamics.

Keywords: Limit order book; stochastic model; quantitative finance; market microstructure; measurevalued process (search for similar items in EconPapers)
Date: 2025
New Economics Papers: this item is included in nep-mst
Note: View the original document on HAL open archive server: https://hal.science/hal-03968767v1
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Published in SIAM Journal on Financial Mathematics, 2025, 16 (1), pp.123-166

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