Mechanics of Good Trade Execution in the Framework of Linear Temporary Market Impact

31 Pages Posted: 2 Oct 2019 Last revised: 8 Jul 2020

See all articles by Claudio Bellani

Claudio Bellani

Imperial College London - Department of Mathematics

Damiano Brigo

Imperial College London - Department of Mathematics

Date Written: July 8, 2020

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.

Keywords: Trade execution, Market impact

JEL Classification: C60

Suggested Citation

Bellani, Claudio and Brigo, Damiano, Mechanics of Good Trade Execution in the Framework of Linear Temporary Market Impact (July 8, 2020). Available at SSRN: https://ssrn.com/abstract=3458454 or http://dx.doi.org/10.2139/ssrn.3458454

Claudio Bellani (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

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