Numerical Methods for an Optimal Order Execution Problem

29 Pages Posted: 5 Jun 2010

See all articles by Fabien Guilbaud

Fabien Guilbaud

Université Paris VII Denis Diderot

Mohamed Mnif

Ecole Nationale d'Ingénieurs de Tunis (ENIT)

Huyên Pham

Université Paris VII Denis Diderot

Date Written: June 3, 2010

Abstract

This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP) equation is a quasi-variational inequality QVI) with solvency constraint satisfied by the value function in the sense of constrained viscosity solutions. By taking advantage of the lag variable tracking the time interval between trades, we can provide an explicit backward numerical scheme for the time discretization of the DPQVI. The convergence of this discrete-time scheme is shown by viscosity solutions arguments. An optimal quantization method is used for computing the (conditional) expectations arising in this scheme. Numerical results are presented by examining the behaviour of optimal liquidation strategies, and comparative performance analysis with respect to some benchmark execution strategies. We also illustrate our optimal liquidation algorithm on real data, and observe various interesting patterns of order execution strategies. Finally, we provide some numerical tests of sensitivity with respect to the bid/ask spread and market impact parameters.

Keywords: Optimal Liquidation, Impulse Control Problem, Quasi-Variational Inequality, Explicit Backward Scheme, Quantization Method, Viscosity Solutions

JEL Classification: G11

Suggested Citation

Guilbaud, Fabien and Mnif, Mohamed and Pham, Huyen, Numerical Methods for an Optimal Order Execution Problem (June 3, 2010). Available at SSRN: https://ssrn.com/abstract=1620400 or http://dx.doi.org/10.2139/ssrn.1620400

Fabien Guilbaud (Contact Author)

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Mohamed Mnif

Ecole Nationale d'Ingénieurs de Tunis (ENIT) ( email )

Tunisia

Huyen Pham

Université Paris VII Denis Diderot ( email )

Batiment Sophie Germain 5 rue Thomas Mann
Paris, 75205
France

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