Optimal trade execution in order books with stochastic liquidity

Antje Fruth, Torsten Schöneborn and Mikhail Urusov

Mathematical Finance, 2019, vol. 29, issue 2, 507-541

Abstract: In financial markets, liquidity changes randomly over time. We consider such random variations of the depth of the order book and evaluate their influence on optimal trade execution strategies. If the stochastic structure of liquidity changes satisfies certain conditions, then the unique optimal trading strategy exhibits a conventional structure with a single wait region and a single buy region, and profitable round‐trip strategies do not exist. In other cases, optimal strategies can feature multiple wait regions and optimal trade sizes that can be decreasing in the size of the position to be liquidated. Furthermore, round‐trip strategies can be profitable depending on bid–ask spread assumptions. We illustrate our findings with several examples including the Cox–Ingersoll–Ross model for the evolution of liquidity.

Date: 2019
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