Optimal execution with non-linear transient market impact. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio
• Is Part Of: Quantitative finance. Volume 17:Issue 1(2017)
• Page Start: 41
• Page End: 54
• Publication Date: 2017-01-02
• Subjects: Optimal execution -- Market impact -- Price manipulation -- Sequential quadratic programming -- Liquidity; C20 -- C61 -- C88 -- D44 -- D47 -- D53; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2016.1181274
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We study the problem of the optimal execution of a large trade in the propagator model with non-linear transient impact. From brute force numerical optimization of the cost functional, we find that the optimal solution for a buy programme 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 non-linear 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; the objective in each case is to robustify the solution in a parsimonious and natural way.