Optimal execution with limit and market orders

Abstract

We develop an optimal execution policy for an investor seeking to execute a large order using limit and market orders. The investor solves the optimal policy considering different restrictions on volume of both types of orders and depth at which limit orders are posted. We show how the execution policies perform when targeting the volume schedule of the Almgren–Chriss execution strategy. The different strategies considered by the investor outperform the Almgren–Chriss price with an average savings per share of about one to two and a half times the spread. This improvement over Almgren–Chriss is due to the strategies benefiting from the optimal mix of limit orders, which earn the spread and market orders, which keep the investor’s inventory schedule on target.

Keywords:

• Algorithmic trading
• High-frequency trading
• Acquisition
• Liquidation
• Impulse control
• TWAP

Acknowledgements

The authors would like to thank Robert Almgren, Frederi G. Viens and an anonymous referee for their comments and discussions of the topic.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

SJ would also like to thank NSERC and GRI for partially funding this work. ÁC acknowledges the research support of the Oxford-Man Institute for Quantitative Finance.