Algorithmic trading in a microstructural limit order book model

Frédéric Abergel (), Côme Huré and Huyên Pham ()
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Frédéric Abergel: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec - Université Paris-Saclay
Côme Huré: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique
Huyên Pham: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique

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Abstract: We propose a microstructural modeling framework for studying optimal market making policies in a FIFO (first in first out) limit order book (LOB). In this context, the limit orders, market orders, and cancel orders arrivals in the LOB are modeled as Cox point processes with intensities that only depend on the state of the LOB. These are high-dimensional models which are realistic from a micro-structure point of view and have been recently developed in the literature. In this context, we consider a market maker who stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price, and identifies the strategies that maximize her P&L penalized by her inventory. We apply the theory of Markov Decision Processes and dynamic programming method to characterize analytically the solutions to our optimal market making problem. The second part of the paper deals with the numerical aspect of the high-dimensional trading problem. We use a control randomization method combined with quantization method to compute the optimal strategies. Several computational tests are performed on simulated data to illustrate the efficiency of the computed optimal strategy. In particular, we simulated an order book with constant/ symmet-ric/ asymmetrical/ state dependent intensities, and compared the computed optimal strategy with naive strategies. Some codes are available on https://github.com/comeh.

Keywords: quantization; local regression; Hawkes Process; pure-jump controlled process; Limit order book; Markov Decision Process; high-frequency trading; high-dimensional stochastic control (search for similar items in EconPapers)
Date: 2020-08-02
New Economics Papers: this item is included in nep-cmp and nep-mst
Note: View the original document on HAL open archive server: https://hal.science/hal-01514987v3
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Citations: View citations in EconPapers (7)

Published in Quantitative Finance, 2020, 20 (8), pp.1263-1283. ⟨10.1080/14697688.2020.1729396⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01514987

DOI: 10.1080/14697688.2020.1729396

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