Are there any studies on the average difference or ratio between Settlement (execution price) and the Spot price dependant on lot size.

I'm looking for a function such as SETTLEMENT=SPOT*LOT_SIZE^CURVING_FACTOR/commodity_constant*ASK/BID.

This settlement/spot ratio is dependent on the amount of liquidity and the commodity type. However the ask/bid spread is also dependent on the amount of liquidity. So I was hoping that the ASK/BID spread would be a good starting point. However I don't have enough knowledge to decide what the best "curving factor" I should use, quadratic/cubic/exponentioal/linear... Is this the correct way to model it?

I have to do this because I'll be working with a system that can't do limit/stop orders and so I need to estimate what the execution price will be before execution.

Example

A 10 quantity lot transaction with a spot of 100 USD/lot could yield a settlement after execution of 1002 USD. This is a .2% increase over the spot rate/lot. However a 100 quantity lot transaction could yield a settlement of 1010 USD giving a 1% increase of the spot.

• This will be very market-specific. The thickness of the market -- the amount of depth as you move away from the market -- will vary a lot, and will certainly be impacted by matching algorithm in use. But, in general, you are asking about "market impact" modeling. Try googling for Robert Almgren's work on it, e.g.: cims.nyu.edu/~almgren/papers/costestim.pdf – RaveTheTadpole Jul 16 '15 at 22:01