I'd like to know how are open and close prices of the mini snp futures contracts determined. For some reason I cannot find an answer to this basic question on the cme website.
By Close do you mean the Last Price? I think what you mean is technically known as the Daily Settlement price at the CME, it is described here
In essence it is based on the combined VWAP of the big S&P and mini S&P in the last 30 seconds. There is a special rule on the last day of the month, which is described separately here
In essence on that day the same procedure is applied, but at 3pm Central time, instead of at the close, i.e. the settlement is 15 minutes before the close. This is to line up the EOM value with the NYSE closing time which is 4pm Eastern or 3 pm Central.
The open price, as far as I know is just the price of the first trade when the market re-opens for the night at 5pm Central, 6pm Eastern. So for example the Open price for the Monday session is the price shortly after 5pm CT Sunday when the Monday trading session begins.
Hope this answers your question.