Impact / slippage model for open and closing crossing auctions?

The general impact model for trading a VWAP order throughout the day has the form of:

$\alpha \cdot \sigma_n \cdot \text{(participation rate)}^\beta$

I'm looking for an impact / slippage model of any form for the open and closing crossing acution for US equities (or any other assetclass).

What would you use instead of $\sigma_n$, and what would you set as a pessimistic estimate or upper bound on $\alpha$ and $\beta$?

I prefer simulations to be careful and pessimistic, therefore any upper bound on these quantitites or even a rule of thumb would help.

• I am no expert in these models, but my impression was that they require certain continuity in time, like being able to trade for the next X hours/minutes for the impact to take place. In case of a closing cross, it's an 1 time event - you submit your order to the cross, and get filled at the close. I don't think it's a matter of picking your params, you need a completele different approach, starting with what you really mean by an impact of the order submitted to the closing cross. – LazyCat Oct 20 '15 at 13:58
• @LazyCat, assume you have 500 / 500 limit orders in the crossing book on both sides, when I enter 1000 more to buy. The crossing price will be most probably different because of my huge additional order. This is the mechanical part of the impact, i.e. knowing the full book and the crossing mechanics this is exactly calculable. Other than this, I can also imagine that someone tracks my order and given my good forecasting power will enter more buy orders to benefit from my alpha (this is less likely or illegal). – Mark Horvath Oct 21 '15 at 0:01
• Two points: first, the imbalances are not printed till some time near the close (3:45pm for NYSE, 3:50pm for NASDAQ, if I recall correctly). So if you enter your order before that, no one sees it, and there is zero immediate impact. Second, once available, these imbalances have a strong impact on the market. So you may look at their historical sizes, say, on stock by stock level, and make sure you don't send too large orders there. – LazyCat Oct 21 '15 at 1:11
• @LazyCat, this is all true, actually expect a negative/reverting effect because of the imbalance mechanism, as is designed so by the exchange to stabilize prices. Nonetheless, irrespective of the imbalance mechanism, putting a big order in the crossing book will move prices against us, which we need to consider in realistic backtests. May have to measure the effect myself, of course. – Mark Horvath Oct 21 '15 at 21:44