Optimal trade execution of equities in a limit order market

Abstract

The paper describes an approach for optimising trade execution in a limit order market. The way a trade is executed becomes important when the trade is a significant proportion of the day's turnover in a particular security. Under these circumstances limited liquidity leads to a significant transaction cost referred to as trade shortfall. We describe a method for calculating a trade execution plan which balances intra-day variations in the supply of liquidity against the risk of adverse future price movements. Our trade execution plans correspond to solutions of discrete time dynamic programming problems. This formulation admits the specification of transaction costs within a Value at Risk framework. The trade execution plans are derived and tested for three popular stocks on the Australian Stock Exchange (ASX). The performance of the plans is evaluated on an out of sample test set of the limit order book for each security and compared to three simpler trade execution strategies.