Price manipulation in a market impact model with dark pool. Issue 5 (3rd September 2017)

• Record Type: Journal Article
• Authors: Klöck, Florian; Schied, Alexander; Sun, Yuemeng
• Is Part Of: Applied mathematical finance. Volume 24:Issue 5(2017)
• Page Start: 417
• Page End: 450
• Publication Date: 2017-09-03
• Subjects: Price manipulation -- transaction-triggered price manipulation -- nonnegative expected liquidation costs -- dark pool -- market impact model -- optimal trade execution -- optimal liquidation; Business mathematics -- Periodicals; 650.0151
• DOI: 10.1080/1350486X.2017.1406438
• Languages: English
• ISSNs: 1350-486X

Abstract

ABSTRACT: For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren–Chriss model. Conditions for the absence of price manipulation for all Almgren–Chriss models include the absence of temporary cross-venue impact, the presence of full permanent cross-venue impact and the additional penalization of orders executed in the dark pool. When a particular Almgren–Chriss model has been fixed, we show by a number of examples that the regularity of the dark-pool model hinges in a subtle way on the interplay of all model parameters and on the liquidation time constraint. The paper can also be seen as a case study for the regularity of market impact models in general.