Strategic Execution Trajectories

33 Pages Posted: 15 Jul 2021

Date Written: April 2, 2021

Abstract


We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact. Various numerical examples are included for illustration, each of which admits a unique optimal solution, however uniqueness in general remains unproven.

Keywords: Block trade, financial markets, market impact, market manipulation, optimal transport, optimal trade execution, optimization, quantitative finance, transactions costs.

JEL Classification: C61, D53, D81.

Suggested Citation

Bordigoni, Giuliana and Figalli, Alessio and Ledford, Anthony and Ustinov, Philipp, Strategic Execution Trajectories (April 2, 2021). Available at SSRN: https://ssrn.com/abstract=3885551 or http://dx.doi.org/10.2139/ssrn.3885551

Giuliana Bordigoni

Man AHL ( email )

Riverbank House
2 Swan Lane
London, EC4R 3AD
United Kingdom

Alessio Figalli

ETH Zurich ( email )

Rämistrasse 101
ETH Zurich
Z√úRICH, 8092
Switzerland

HOME PAGE: http://people.math.ethz.ch/~afigalli/

Anthony Ledford (Contact Author)

Man AHL ( email )

Riverbank House
2 Swan Lane
London, EC4R 3AD
United Kingdom

HOME PAGE: http://www.ahl.com

Philipp Ustinov

Man Group plc ( email )

2 Swan Lane
London, EC4R 3AD
United Kingdom

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