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
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.
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.