High-Resilience Limits of Block-Shaped Order Books

12 Pages Posted: 27 Sep 2014

See all articles by Jan Kallsen

Jan Kallsen

Munich University of Technology

Johannes Muhle-Karbe

Carnegie Mellon University - Department of Mathematical Sciences

Date Written: September 25, 2014

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.

Keywords: Limit order books; price impact; high-resilience limit

JEL Classification: G11, G12

Suggested Citation

Kallsen, Jan and Muhle-Karbe, Johannes, High-Resilience Limits of Block-Shaped Order Books (September 25, 2014). Swiss Finance Institute Research Paper No. 14-72. Available at SSRN: https://ssrn.com/abstract=2501362 or http://dx.doi.org/10.2139/ssrn.2501362

Jan Kallsen

Munich University of Technology ( email )

Arcisstrasse 21
Munich, 80333
Germany

Johannes Muhle-Karbe (Contact Author)

Carnegie Mellon University - Department of Mathematical Sciences ( email )

Pittsburgh, PA 15213-3890
United States

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