Optimal Order Scheduling for Deterministic Liquidity Patterns

TL;DR

This paper develops an explicit optimal order scheduling strategy for large trades considering deterministic variations in market liquidity, improving execution cost minimization over static models.

Contribution

It introduces a novel model allowing liquidity parameters to vary deterministically and provides an explicit solution using convex analysis techniques.

Findings

Explicit optimal scheduling strategy derived

Model accounts for deterministic liquidity variations

Solution improves trade execution cost management

Abstract

We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By contrast to the previous literature, see, e.g., Obizhaeva and Wang (2005), Predoiu, Shaikhet, and Shreve (2011), we allow the liquidity parameters of market depth and resilience to vary deterministically over the course of the trading period. The resulting singular optimal control problem is shown to be tractable by methods from convex analysis and, under minimal assumptions, we construct an explicit solution to the scheduling problem in terms of some concave envelope of the resilience adjusted market depth.