Optimal Liquidation in a Level-I Limit Order Book for Large Tick Stocks

27 Pages Posted: 8 Jan 2017 Last revised: 15 Nov 2017

See all articles by Antoine (Jack) Jacquier

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Hao Liu

Imperial College London

Date Written: January 7, 2017

Abstract

We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with the spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on the most recent price move direction. Our goal is to maximise the expected terminal wealth of an agent who needs to liquidate her positions within a fixed time horizon. By assuming that the agent trades (through both limit and market orders) only when the price moves, we model her liquidation procedure as a semi-Markov decision process, and compute the semi-Markov kernel using Laplace method in the language of queueing theory. The optimal liquidation policy is then solved by dynamic programming, and illustrated numerically.

Keywords: limit order book, optimal liquidation, semi-Markov decision process, queueing theory, dynamic programming

JEL Classification: C44, C61, C51

Suggested Citation

Jacquier, Antoine and Liu, Hao, Optimal Liquidation in a Level-I Limit Order Book for Large Tick Stocks (January 7, 2017). Available at SSRN: https://ssrn.com/abstract=2895765 or http://dx.doi.org/10.2139/ssrn.2895765

Antoine Jacquier

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Hao Liu (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

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