Price manipulation in a market impact model with dark pool

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
• nonnegative expected liquidation costs
• dark pool
• market impact model
• optimal trade execution
• optimal liquidation

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Restricting the size of a matching order by setting a minimum quantity level $M$ is a common feature in many dark pools. For instance, it helps to protect against ‘fishing’ by predatory traders; see Mittal (2008).

2. If at time $t=0$ the dark pool contains an order ${\tilde{Y}}_0$ of the opposite side, then the investor could fill this order immediately and then start liquidating the remaining asset position $X_0-{\tilde{Y}}_0$, maybe by resizing the dark-pool order. Therefore, we can assume that the dark pool does not contain a matching order at $t=0$. Moreover, restricting the placement of dark-pool orders to $t=0$ lets us exclude so-called ‘fishing strategies; see Remark 3.5 below.

Additional information

Funding

F.K. and A.S. gratefully acknowledge support by Deutsche Forschungsgemeinschaft (DFG) through Research Grant [SCHI 500/3-1].