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How should I use central banks rates in order to compute 2-day forward exchange rate on EURUSD

Good morning, I would like to compute a 2-day forward exchange rate on EURUSD. For that, I have historical data on EURUSD spot price, and I know that theoretically, when maturity is T we have : ...
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Settlement/Spot/(bid ask spread) ratio

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 ...