Optimal Limit-versus-Market Order Slicing Under a VWAP Benchmark - Continuous Case

Abstract

Algorithmic brokers benchmarked to TWAP or VWAP face a limit-order market-order tradeoff when slicing orders. Executing market orders keeps them on schedule but is costly. Executing limit orders saves spread but can lead to schedule slippage. We build on our results in the discrete shares case Li [2012] to present an optimal solution for execution in light of this tradeoff in the limit of continuous shares. As in the discrete case, the optimal solution is described in terms of a forward and backward boundary which define how many limit orders should be placed on the order book and when to execute market orders. Closed-form solutions for the boundaries are derived for the “stationary limit.” These boundaries can be computed numerically in the general case.