An Algebraic Framework for the Modeling of Limit Order Books

Fuente: arXiv
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Main Authors: Bleher, Johannes, Bleher, Michael
Format: Preprint
Published: 2024
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author Bleher, Johannes
Bleher, Michael
author_facet Bleher, Johannes
Bleher, Michael
contents Introducing an algebraic framework for modeling limit order books (LOBs) with tools from physics and stochastic processes, our proposed framework captures the creation and annihilation of orders, order matching, and the time evolution of the LOB state. It also enables compositional settings, accommodating the interaction of heterogeneous traders and different market structures. We employ Dirac notation and generalized generating functions to describe the state space and dynamics of LOBs. The utility of this framework is shown through simulations of simplified market scenarios, illustrating how variations in trader behavior impact key market observables such as spread, return volatility, and liquidity. The algebraic representation allows for exact simulations using the Gillespie algorithm, providing a robust tool for exploring the implications of market design and policy changes on LOB dynamics. Future research can expand this framework to incorporate more complex order types, adaptive event rates, and multi-asset trading environments, offering deeper insights into market microstructure and trader behavior and estimation of key drivers for market microstructure dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2406_04969
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An Algebraic Framework for the Modeling of Limit Order Books
Bleher, Johannes
Bleher, Michael
Trading and Market Microstructure
Mathematical Finance
Statistical Finance
60G10, 62M10, 91B26, 65C40
G.3; I.6.1; I.6.4; J.4
Introducing an algebraic framework for modeling limit order books (LOBs) with tools from physics and stochastic processes, our proposed framework captures the creation and annihilation of orders, order matching, and the time evolution of the LOB state. It also enables compositional settings, accommodating the interaction of heterogeneous traders and different market structures. We employ Dirac notation and generalized generating functions to describe the state space and dynamics of LOBs. The utility of this framework is shown through simulations of simplified market scenarios, illustrating how variations in trader behavior impact key market observables such as spread, return volatility, and liquidity. The algebraic representation allows for exact simulations using the Gillespie algorithm, providing a robust tool for exploring the implications of market design and policy changes on LOB dynamics. Future research can expand this framework to incorporate more complex order types, adaptive event rates, and multi-asset trading environments, offering deeper insights into market microstructure and trader behavior and estimation of key drivers for market microstructure dynamics.
title An Algebraic Framework for the Modeling of Limit Order Books
topic Trading and Market Microstructure
Mathematical Finance
Statistical Finance
60G10, 62M10, 91B26, 65C40
G.3; I.6.1; I.6.4; J.4
url https://arxiv.org/abs/2406.04969