Static vs adapted optimal execution strategies in two benchmark trading models

TL;DR

This paper compares static and adaptive optimal trade execution strategies in two benchmark models, finding that static strategies are nearly optimal except in extreme cases, thus supporting their practical use.

Contribution

It derives static optimal strategies for two benchmark models and quantitatively compares their performance to fully adapted strategies.

Findings

Static strategies perform nearly as well as adaptive ones in most cases.

The difference between static and adaptive strategies is negligible except in extreme scenarios.

Supports the use of static strategies for practical optimal trade execution.

Abstract

We consider the optimal solutions to the trade execution problem in the two different classes of i) fully adapted or adaptive and ii) deterministic or static strategies, comparing them. We do this in two different benchmark models. The first model is a discrete time framework with an information flow process, dealing with both permanent and temporary impact, minimizing the expected cost of the trade. The second model is a continuous time framework where the objective function is the sum of the expected cost and a value at risk (or expected shortfall) type risk criterion. Optimal adapted solutions are known in both frameworks from the original works of Bertsimas and Lo (1998) and Gatheral and Schied (2011). In this paper we derive the optimal static strategies for both benchmark models and we study quantitatively the improvement in optimality when moving from static strategies to fully adapted ones. We conclude that, in the benchmark models we study, the difference is not relevant, except for extreme unrealistic cases for the model or impact parameters. This indirectly confirms that in the similar framework of Almgren and Chriss (2000) one is fine deriving a static optimal solution, as done by those authors, as opposed to a fully adapted one, since the static solution happens to be tractable and known in closed form.