Price Manipulation in a Market Impact Model with Dark Pool
28 Pages Posted: 19 Mar 2011 Last revised: 19 Jul 2017
Date Written: August 25, 2011
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.
Keywords: Price manipulation, transaction-triggered price manipulation, positive expected liquidation costs, dark pool, market impact model, optimal order execution, optimal liquidation
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