Optimal Execution with Nonlinear Transient Market Impact

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