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      Algorithmic trading in a microstructural limit order book model

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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.

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          Most cited references 8

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          Optimal dealer pricing under transactions and return uncertainty

           Thomas Ho,  Hans Stoll (1981)
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            A Stochastic Model for Order Book Dynamics

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              High-frequency trading in a limit order book

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                Author and article information

                Journal
                2017-05-03
                Article
                1705.01446

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                q-fin.TR math.PR
                ccsd

                Probability, Trading & Market microstructure

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