Optimal execution with non-linear transient market impact

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 separat...

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Bibliographic Details
Published in:Quantitative finance 2017-01, Vol.17 (1), p.41-54
Main Authors: Curato, Gianbiagio, Gatheral, Jim, Lillo, Fabrizio
Format: Article
Language:English
Subjects:
Liquidity
Market impact
Optimal execution
Price manipulation
Sequential quadratic programming
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Summary: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.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2016.1181274