Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions

Brunovsky, P., Černý, A. & Komadel, J. (2018). Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions. European Journal of Operational Research, 264(3), pp. 1159-1171. doi: 10.1016/j.ejor.2017.07.054

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Abstract

We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the liquidation time horizon becomes a stopping time determined endogenously, as part of the optimal strategy. We find that the optimal liquidation strategy is consistent with the square-root law which states that the average price impact per share is proportional to the square root of the size of the meta-order (Bershova and Rakhlin, 2013; Farmer et al., 2013; Donier et al., 2015; T´oth et al., 2016).

Mathematically, the Hamilton-Jacobi-Bellman equation of our optimization leads to a severely singular and numerically unstable ordinary differential equation initial value problem. We provide careful analysis of related singular mixed boundary value problems and devise a numerically stable computation strategy by re-introducing time dimension into an otherwise time-homogeneous task.

Item Type: Article
Additional Information: © 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: finance, optimal liquidation, price impact, square-root law, singular boundary value problem, stochastic optimal control
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/17877

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