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

TL;DR

This paper introduces robust, adaptive trade execution strategies that minimize pathwise trading costs using Young differential equations, without requiring full asset price dynamics, especially useful in volatile markets.

Contribution

It constructs explicit, adaptive good trade execution strategies based on Young differential equations, minimizing pathwise costs without full SDE specifications.

Findings

Strategies are reactive to actual price paths.

Methods are robust across different market models.

Strategies are implementable via initial value problems.

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.