Calibration of optimal execution of financial transactions in the presence of transient market impact

TL;DR

This paper models and calibrates optimal execution strategies in financial markets considering transient market impact, providing analytical solutions and real data calibration for both risk-neutral and risk-averse investors.

Contribution

It introduces a calibration method for a market impact model that accounts for volume and temporal effects, enhancing optimal execution strategies.

Findings

Analytical solutions for optimal execution under the impact model.

Calibration of the impact model with real market data.

Regularization of solutions when including spread costs.

Abstract

Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud et al., 2004), which has the property of describing both the volume and the temporal dependence of price change due to trading. We show how this model can be used to describe price impact also in aggregated trade time or in real time. We then solve analytically and calibrate with real data the optimal execution problem both for risk neutral and for risk averse investors and we derive an efficient frontier of optimal execution. When we include spread costs the problem must be solved numerically and we show that the introduction of such costs regularizes the solution.