Static vs Adapted Optimal Execution Strategies in Two Benchmark Trading Models

51 Pages Posted: 21 Sep 2016

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Clément Piat

Imperial College London - Department of Mathematics

Date Written: September 18, 2016

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.

Keywords: Optimal Trade Execution, Optimal Scheduling, Algorithmic Trading, Calculus of Variations, Risk Measures, Value at Risk, Market Impact, Permanent Impact, Temporary Impact, Static Solutions, Adapted Solutions, Dynamic Programming

JEL Classification: C51, G12, G13

Suggested Citation

Brigo, Damiano and Piat, Clément, Static vs Adapted Optimal Execution Strategies in Two Benchmark Trading Models (September 18, 2016). Available at SSRN: https://ssrn.com/abstract=2840290 or http://dx.doi.org/10.2139/ssrn.2840290

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

Clément Piat (Contact Author)

Imperial College London - Department of Mathematics ( email )

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

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