OPTIMAL EXECUTION COST FOR LIQUIDATION THROUGH A LIMIT ORDER MARKET

Etienne Chevalier (), Vathana Ly Vath (), Simone Scotti () and Alexandre Roch ()
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Etienne Chevalier: Laboratoire de Mathématiques et Modélisation d’Evry, Université d’Evry, Bâtiment I.B.G.B.I., 3e étage, 23 Bd. de France, 91037 Evry Cedex, France
Vathana Ly Vath: #x2020;Ecole Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise, 1, Square de la Résistance, 91025 Evry Cedex, France
Simone Scotti: #x2021;Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot, 4, Place Jussieu, Avenue de France, 75205 Paris Cedex 13, France
Alexandre Roch: #xA7;Finance Department, University of Quebec in Montreal, 315, Sainte-Catherine Street East, Montreal, Quebec, Canada, H2X 3X2, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 01, 1-26

Abstract: We study the problem of optimally liquidating a large portfolio position in a limit-order 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 process, and the market-order arrival process as a controlled 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 variational inequalities. We conclude with a calibration of the model on recent market data and a numerical implementation.

Keywords: Liquidity risk; limit-order books; impulse control; viscosity solutions; variational inequalities (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219024916500047

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