Optimal Execution Cost for Liquidation Through a Limit Order Market

28 Pages Posted: 30 Nov 2013 Last revised: 26 Apr 2017

Etienne Chevalier

Université de Marne-la-Vallée

Vathana Ly Vath

Université d'Évry

Alexandre F. Roch

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG)

Simone Scotti

Université Paris VII Denis Diderot

Date Written: July 9, 2015

Abstract

We study the problem of optimally liquidating a large portfolio position in a limit order book market. We allow for both limit and market orders and the optimal solution is a combination of both types of orders. Market orders deplete the order book, making future trades more expensive, whereas limit orders can be entered at more favorable prices but are not guaranteed to be filled. We model the bid-ask spread with resilience by a jump-diffusion process, and the market order arrival process as a Poisson process. The objective is to minimize the execution cost of the strategy. We formulate the problem as a mixed stochastic continuous control and impulse problem for which the value function is shown to be the unique viscosity solution of the associated system of variational inequalities. We conclude with a calibration of the model on recent market data.

Keywords: Liquidity Risk, Limit Order Books, Impulse Control, Viscosity Solutions, System of Variational Inequalities

JEL Classification: D40, G11

Suggested Citation

Chevalier, Etienne and Ly Vath, Vathana and Roch, Alexandre F. and Scotti, Simone, Optimal Execution Cost for Liquidation Through a Limit Order Market (July 9, 2015). Available at SSRN: https://ssrn.com/abstract=2361110 or http://dx.doi.org/10.2139/ssrn.2361110

Etienne Chevalier

Université de Marne-la-Vallée ( email )

6-8 Cours du Danube
5, Bd Descartes
Serris, Marne-la-Vallée Cedex 2 77700
France

Vathana Ly Vath

Université d'Évry ( email )

Bd. François Mitterrand
F-91025 Evry Cedex, 91028
France

Alexandre F. Roch (Contact Author)

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG) ( email )

Case postale 8888
Succursale Centre-ville
Montreal, Quebec H3C 3P8
Canada

Simone Scotti

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

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