High-Resilience Limits of Block-Shaped Order Books

TL;DR

This paper demonstrates that wealth processes in block-shaped order book models converge to those in reduced-form models as resilience increases, simplifying portfolio optimization in highly-resilient markets.

Contribution

It establishes a limit theorem connecting block-shaped order book models with reduced-form models, enabling easier portfolio choice analysis in high-resilience scenarios.

Findings

Wealth processes converge as resilience tends to infinity.

Portfolio optimization simplifies in highly-resilient models.

Theoretical link between two prominent market models.

Abstract

We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this limit theorem, we explain how to reduce portfolio choice in highly-resilient Obizhaeva/Wang models to the corresponding problem in an Almgren/Chriss setup with small quadratic trading costs.