With all other factors held constant, how can I determine the decrease in SPX index due to dividends until the expiration date of my options contract? For example, if my contract expires in 14 days, can I just take the S&P dividend yield of 1.8% and multiply by (14/365)? Or is it more accurate to find out which specific companies will be paying dividends in the next 14 days and use those actual values? I'm mainly wondering how big investment firms do it for SPX options, and if there are any reasonable short cuts for retail investors.
That dog won't bark! The impact of dividends on SPX options is a continuous function, not discrete, like on SPY options. I think you may be seeking the PVDiv value, to aid in properly computing impact on the options. The price you submit to your BSM for underlying can be used to compensate for the impact of dividends (allowing the "dividend" value to your BSM to be set to zero). U=(SPOT-PVDiv), where U is the value used for the underlying in the BSM. There is a process for more directly extracting "U" from each chain, but may be more than you desire to tackle. (PVDiv=PresentValue of the Dividend). Note: since process exists for solving for U, the value of PVDiv is simply(SPOT-U), if you need to compute it.
If you want to be exact you need to find all 500 names and who goes ex div on what dates and what their weighting is and do the calculations.
If the futures+options expire on the same date, and you're only 14 days out, the difference between the spot month and cash could give you a good proxy.
Many years ago the CBOE used to publish this information. Not sure if they still do. I used to get a sheet for the OEX which listed dividends on each day.