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Mechanics of good trade execution in the framework of linear temporary market impact

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  • Claudio Bellani
  • Damiano Brigo

Abstract

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; this is paramount in volatile regimes, where price trajectories can considerably deviate from their expected value. Remarkably however, the implementation of our strategies does not require the full specification of an SDE evolution for the traded asset price, making them robust across different models. Moreover, rather than minimising the expected trading cost, good trade execution strategies minimise trading costs in a pathwise sense, a point of view not yet considered in the literature. The mathematical apparatus for such a pathwise minimisation hinges on certain random Young differential equations that correspond to the Euler-Lagrange equations of the classical Calculus of Variations. These Young differential equations characterise our good trade execution strategies in terms of an initial value problem that allows for easy implementations.

Suggested Citation

  • Claudio Bellani & Damiano Brigo, 2019. "Mechanics of good trade execution in the framework of linear temporary market impact," Papers 1909.10464, arXiv.org, revised Jul 2020.
  • Handle: RePEc:arx:papers:1909.10464
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    References listed on IDEAS

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    1. Christoph Belak & Johannes Muhle-Karbe & Kevin Ou, 2018. "Optimal Trading with General Signals and Liquidation in Target Zone Models," Papers 1808.00515, arXiv.org.
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