[1205.4008] Price manipulation in a market impact model with dark pool

[1205.4008] Price manipulation in a market impact model with dark pool:

 "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."

"We have analyzed the regularity of a class of dark-pool extensions of an Almgren–Chriss model and found that such models admit price manipulation strategies unless the model parameters satisfy certain restrictions. The corresponding parameter values will typically differ strongly from values found in empirical analysis or calibration of real-world dark pools. Our results can therefore provide some indication that dark pools may create market inefficiencies and disturb the price finding mechanism of markets."

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