Optimal Execution with Nonlinear Transient Market Impact

Quantitative Finance, Vol. 17, No. 1, 41-54, 2017

29 Pages Posted: 17 Dec 2014 Last revised: 25 Feb 2017

See all articles by Gianbiagio Curato

Gianbiagio Curato

Scuola Normale Superiore

Jim Gatheral

CUNY Baruch College

Fabrizio Lillo

Università di Bologna

Date Written: October 6, 2015

Abstract

We study the problem of the optimal execution of a large trade in the propagator model with nonlinear transient impact. From brute force numerical optimization of the cost functional, we find that the optimal solution for a buy program typically features a few short intense buying periods separated by long periods of weak selling. Indeed, in some cases we find negative expected cost. We show that this undesirable characteristic of the nonlinear transient impact model may be mitigated either by introducing a bid-ask spread cost or by imposing convexity of the instantaneous market impact function for large trading rates.

Keywords: Transient price impact, market impact model, optimal order execution, transaction‐triggered price manipulation, homotopy analysis, SQP algorithm, GSS algorithm

Suggested Citation

Curato, Gianbiagio and Gatheral, Jim and Lillo, Fabrizio, Optimal Execution with Nonlinear Transient Market Impact (October 6, 2015). Quantitative Finance, Vol. 17, No. 1, 41-54, 2017. Available at SSRN: https://ssrn.com/abstract=2539240 or http://dx.doi.org/10.2139/ssrn.2539240

Gianbiagio Curato

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Jim Gatheral

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

Fabrizio Lillo (Contact Author)

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

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